Finite Math Examples

$[\begin{array}{c} 15 & - 27 & - 28 \\ 45 & 25 & 10 \\ 41 & - 19 & 22 \end{array}] [\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} - 13 \\ - 11 \\ 24 \end{array}]$

Step 1

Multiply $[\begin{array}{c} 15 & - 27 & - 28 \\ 45 & 25 & 10 \\ 41 & - 19 & 22 \end{array}] [\begin{array}{c} x \\ y \\ z \end{array}]$ .

Tap for more steps...

Step 1.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is $3 \times 3$ and the second matrix is $3 \times 1$ .

Step 1.2

Multiply each row in the first matrix by each column in the second matrix.

$[\begin{array}{c} 15 x - 27 y - 28 z \\ 45 x + 25 y + 10 z \\ 41 x - 19 y + 22 z \end{array}] = [\begin{array}{c} - 13 \\ - 11 \\ 24 \end{array}]$

Step 2

Write as a linear system of equations.

$15 x - 27 y - 28 z = - 13$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3

Solve the system of equations.

Tap for more steps...

Step 3.1

Solve for $x$ in $15 x - 27 y - 28 z = - 13$ .

Tap for more steps...

Step 3.1.1

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 3.1.1.1

Add $27 y$ to both sides of the equation.

$15 x - 28 z = - 13 + 27 y$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3.1.1.2

Add $28 z$ to both sides of the equation.

$15 x = - 13 + 27 y + 28 z$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

$15 x = - 13 + 27 y + 28 z$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3.1.2

Divide each term in $15 x = - 13 + 27 y + 28 z$ by $15$ and simplify.

Tap for more steps...

Step 3.1.2.1

Divide each term in $15 x = - 13 + 27 y + 28 z$ by $15$ .

$\frac{15 x}{15} = \frac{- 13}{15} + \frac{27 y}{15} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3.1.2.2

Simplify the left side.

Tap for more steps...

Step 3.1.2.2.1

Cancel the common factor of $15$ .

Tap for more steps...

Step 3.1.2.2.1.1

Cancel the common factor.

$\frac{15 x}{15} = \frac{- 13}{15} + \frac{27 y}{15} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3.1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 13}{15} + \frac{27 y}{15} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

$x = \frac{- 13}{15} + \frac{27 y}{15} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

$x = \frac{- 13}{15} + \frac{27 y}{15} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3.1.2.3

Simplify the right side.

Tap for more steps...

Step 3.1.2.3.1

Simplify each term.

Tap for more steps...

Step 3.1.2.3.1.1

Move the negative in front of the fraction.

$x = - \frac{13}{15} + \frac{27 y}{15} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3.1.2.3.1.2

Cancel the common factor of $27$ and $15$ .

Tap for more steps...

Step 3.1.2.3.1.2.1

Factor $3$ out of $27 y$ .

$x = - \frac{13}{15} + \frac{3 (9 y)}{15} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3.1.2.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.3.1.2.2.1

Factor $3$ out of $15$ .

$x = - \frac{13}{15} + \frac{3 (9 y)}{3 (5)} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3.1.2.3.1.2.2.2

Cancel the common factor.

$x = - \frac{13}{15} + \frac{3 (9 y)}{3 \cdot 5} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3.1.2.3.1.2.2.3

Rewrite the expression.

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$45 x + 25 y + 10 z = - 11$

$41 x - 19 y + 22 z = 24$

Step 3.2

Replace all occurrences of $x$ with $- \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$ in each equation.

Tap for more steps...

Step 3.2.1

Replace all occurrences of $x$ in $45 x + 25 y + 10 z = - 11$ with $- \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$ .

$45 (- \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Simplify $45 (- \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}) + 25 y + 10 z$ .

Tap for more steps...

Step 3.2.2.1.1

Simplify each term.

Tap for more steps...

Step 3.2.2.1.1.1

Apply the distributive property.

$45 (- \frac{13}{15}) + 45 (\frac{9 y}{5}) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2

Simplify.

Tap for more steps...

Step 3.2.2.1.1.2.1

Cancel the common factor of $15$ .

Tap for more steps...

Step 3.2.2.1.1.2.1.1

Move the leading negative in $- \frac{13}{15}$ into the numerator.

$45 (\frac{- 13}{15}) + 45 (\frac{9 y}{5}) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.1.2

Factor $15$ out of $45$ .

$15 (3) (\frac{- 13}{15}) + 45 (\frac{9 y}{5}) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.1.3

Cancel the common factor.

$15 \cdot (3 (\frac{- 13}{15})) + 45 (\frac{9 y}{5}) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.1.4

Rewrite the expression.

$3 \cdot - 13 + 45 (\frac{9 y}{5}) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

$3 \cdot - 13 + 45 (\frac{9 y}{5}) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.2

Multiply $3$ by $- 13$ .

$- 39 + 45 (\frac{9 y}{5}) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.2.2.1.1.2.3.1

Factor $5$ out of $45$ .

$- 39 + 5 (9) (\frac{9 y}{5}) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.3.2

Cancel the common factor.

$- 39 + 5 \cdot (9 (\frac{9 y}{5})) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.3.3

Rewrite the expression.

$- 39 + 9 (9 y) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

$- 39 + 9 (9 y) + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.4

Multiply $9$ by $9$ .

$- 39 + 81 y + 45 (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.5

Cancel the common factor of $15$ .

Tap for more steps...

Step 3.2.2.1.1.2.5.1

Factor $15$ out of $45$ .

$- 39 + 81 y + 15 (3) (\frac{28 z}{15}) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.5.2

Cancel the common factor.

$- 39 + 81 y + 15 \cdot (3 (\frac{28 z}{15})) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.5.3

Rewrite the expression.

$- 39 + 81 y + 3 (28 z) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

$- 39 + 81 y + 3 (28 z) + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.1.2.6

Multiply $28$ by $3$ .

$- 39 + 81 y + 84 z + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

$- 39 + 81 y + 84 z + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

$- 39 + 81 y + 84 z + 25 y + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 3.2.2.1.2.1

Add $81 y$ and $25 y$ .

$- 39 + 106 y + 84 z + 10 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.2.1.2.2

Add $84 z$ and $10 z$ .

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$41 x - 19 y + 22 z = 24$

Step 3.2.3

Replace all occurrences of $x$ in $41 x - 19 y + 22 z = 24$ with $- \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$ .

$41 (- \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}) - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4

Simplify the left side.

Tap for more steps...

Step 3.2.4.1

Simplify $41 (- \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}) - 19 y + 22 z$ .

Tap for more steps...

Step 3.2.4.1.1

Simplify each term.

Tap for more steps...

Step 3.2.4.1.1.1

Apply the distributive property.

$41 (- \frac{13}{15}) + 41 (\frac{9 y}{5}) + 41 (\frac{28 z}{15}) - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.1.2

Simplify.

Tap for more steps...

Step 3.2.4.1.1.2.1

Multiply $41 (- \frac{13}{15})$ .

Tap for more steps...

Step 3.2.4.1.1.2.1.1

Multiply $- 1$ by $41$ .

$- 41 (\frac{13}{15}) + 41 (\frac{9 y}{5}) + 41 (\frac{28 z}{15}) - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.1.2.1.2

Combine $- 41$ and $\frac{13}{15}$ .

$\frac{- 41 \cdot 13}{15} + 41 (\frac{9 y}{5}) + 41 (\frac{28 z}{15}) - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.1.2.1.3

Multiply $- 41$ by $13$ .

$\frac{- 533}{15} + 41 (\frac{9 y}{5}) + 41 (\frac{28 z}{15}) - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$\frac{- 533}{15} + 41 (\frac{9 y}{5}) + 41 (\frac{28 z}{15}) - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.1.2.2

Multiply $41 \frac{9 y}{5}$ .

Tap for more steps...

Step 3.2.4.1.1.2.2.1

Combine $41$ and $\frac{9 y}{5}$ .

$\frac{- 533}{15} + \frac{41 (9 y)}{5} + 41 (\frac{28 z}{15}) - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.1.2.2.2

Multiply $9$ by $41$ .

$\frac{- 533}{15} + \frac{369 y}{5} + 41 (\frac{28 z}{15}) - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$\frac{- 533}{15} + \frac{369 y}{5} + 41 (\frac{28 z}{15}) - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.1.2.3

Multiply $41 \frac{28 z}{15}$ .

Tap for more steps...

Step 3.2.4.1.1.2.3.1

Combine $41$ and $\frac{28 z}{15}$ .

$\frac{- 533}{15} + \frac{369 y}{5} + \frac{41 (28 z)}{15} - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.1.2.3.2

Multiply $28$ by $41$ .

$\frac{- 533}{15} + \frac{369 y}{5} + \frac{1148 z}{15} - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$\frac{- 533}{15} + \frac{369 y}{5} + \frac{1148 z}{15} - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$\frac{- 533}{15} + \frac{369 y}{5} + \frac{1148 z}{15} - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.1.3

Move the negative in front of the fraction.

$- \frac{533}{15} + \frac{369 y}{5} + \frac{1148 z}{15} - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{533}{15} + \frac{369 y}{5} + \frac{1148 z}{15} - 19 y + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.2

To write $- 19 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{369 y}{5} - 19 y \cdot \frac{5}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.3

Simplify terms.

Tap for more steps...

Step 3.2.4.1.3.1

Combine $- 19 y$ and $\frac{5}{5}$ .

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{369 y}{5} + \frac{- 19 y \cdot 5}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.3.2

Combine the numerators over the common denominator.

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{369 y - 19 y \cdot 5}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{369 y - 19 y \cdot 5}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.4

Simplify each term.

Tap for more steps...

Step 3.2.4.1.4.1

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1.4.1.1

Factor $y$ out of $369 y - 19 y \cdot 5$ .

Tap for more steps...

Step 3.2.4.1.4.1.1.1

Factor $y$ out of $369 y$ .

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{y \cdot 369 - 19 y \cdot 5}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.4.1.1.2

Factor $y$ out of $- 19 y \cdot 5$ .

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{y \cdot 369 + y (- 19 \cdot 5)}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.4.1.1.3

Factor $y$ out of $y \cdot 369 + y (- 19 \cdot 5)$ .

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{y (369 - 19 \cdot 5)}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{y (369 - 19 \cdot 5)}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.4.1.2

Multiply $- 19$ by $5$ .

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{y (369 - 95)}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.4.1.3

Subtract $95$ from $369$ .

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{y \cdot 274}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{y \cdot 274}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.4.2

Move $274$ to the left of $y$ .

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{274 y}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{533}{15} + \frac{1148 z}{15} + \frac{274 y}{5} + 22 z = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.5

To write $22 z$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$- \frac{533}{15} + \frac{274 y}{5} + \frac{1148 z}{15} + 22 z \cdot \frac{15}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.6

Combine $22 z$ and $\frac{15}{15}$ .

$- \frac{533}{15} + \frac{274 y}{5} + \frac{1148 z}{15} + \frac{22 z \cdot 15}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.7

Combine the numerators over the common denominator.

$- \frac{533}{15} + \frac{274 y}{5} + \frac{1148 z + 22 z \cdot 15}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.8

Combine the numerators over the common denominator.

$\frac{- 533 + 1148 z + 22 z \cdot 15}{15} + \frac{274 y}{5} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.9

Multiply $15$ by $22$ .

$\frac{- 533 + 1148 z + 330 z}{15} + \frac{274 y}{5} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.10

Add $1148 z$ and $330 z$ .

$\frac{- 533 + 1478 z}{15} + \frac{274 y}{5} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.11

To write $\frac{274 y}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{- 533 + 1478 z}{15} + \frac{274 y}{5} \cdot \frac{3}{3} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.12

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.2.4.1.12.1

Multiply $\frac{274 y}{5}$ by $\frac{3}{3}$ .

$\frac{- 533 + 1478 z}{15} + \frac{274 y \cdot 3}{5 \cdot 3} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.12.2

Multiply $5$ by $3$ .

$\frac{- 533 + 1478 z}{15} + \frac{274 y \cdot 3}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$\frac{- 533 + 1478 z}{15} + \frac{274 y \cdot 3}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.13

Combine the numerators over the common denominator.

$\frac{- 533 + 1478 z + 274 y \cdot 3}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.14

Multiply $3$ by $274$ .

$\frac{- 533 + 1478 z + 822 y}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.15

Rewrite $- 533$ as $- 1 (533)$ .

$\frac{- 1 \cdot 533 + 1478 z + 822 y}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.16

Factor $- 1$ out of $1478 z$ .

$\frac{- 1 \cdot 533 - (- 1478 z) + 822 y}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.17

Factor $- 1$ out of $- 1 (533) - (- 1478 z)$ .

$\frac{- 1 (533 - 1478 z) + 822 y}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.18

Factor $- 1$ out of $822 y$ .

$\frac{- 1 (533 - 1478 z) - (- 822 y)}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.19

Factor $- 1$ out of $- 1 (533 - 1478 z) - (- 822 y)$ .

$\frac{- 1 (533 - 1478 z - 822 y)}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.2.4.1.20

Move the negative in front of the fraction.

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$- 39 + 106 y + 94 z = - 11$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3

Solve for $y$ in $- 39 + 106 y + 94 z = - 11$ .

Tap for more steps...

Step 3.3.1

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 3.3.1.1

Add $39$ to both sides of the equation.

$106 y + 94 z = - 11 + 39$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.1.2

Subtract $94 z$ from both sides of the equation.

$106 y = - 11 + 39 - 94 z$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.1.3

Add $- 11$ and $39$ .

$106 y = 28 - 94 z$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$106 y = 28 - 94 z$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2

Divide each term in $106 y = 28 - 94 z$ by $106$ and simplify.

Tap for more steps...

Step 3.3.2.1

Divide each term in $106 y = 28 - 94 z$ by $106$ .

$\frac{106 y}{106} = \frac{28}{106} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.2.1

Cancel the common factor of $106$ .

Tap for more steps...

Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{106 y}{106} = \frac{28}{106} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{28}{106} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$y = \frac{28}{106} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$y = \frac{28}{106} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.3

Simplify the right side.

Tap for more steps...

Step 3.3.2.3.1

Simplify each term.

Tap for more steps...

Step 3.3.2.3.1.1

Cancel the common factor of $28$ and $106$ .

Tap for more steps...

Step 3.3.2.3.1.1.1

Factor $2$ out of $28$ .

$y = \frac{2 (14)}{106} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 3.3.2.3.1.1.2.1

Factor $2$ out of $106$ .

$y = \frac{2 \cdot 14}{2 \cdot 53} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 14}{2 \cdot 53} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{14}{53} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$y = \frac{14}{53} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$y = \frac{14}{53} + \frac{- 94 z}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.3.1.2

Cancel the common factor of $- 94$ and $106$ .

Tap for more steps...

Step 3.3.2.3.1.2.1

Factor $2$ out of $- 94 z$ .

$y = \frac{14}{53} + \frac{2 (- 47 z)}{106}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 3.3.2.3.1.2.2.1

Factor $2$ out of $106$ .

$y = \frac{14}{53} + \frac{2 (- 47 z)}{2 (53)}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.3.1.2.2.2

Cancel the common factor.

$y = \frac{14}{53} + \frac{2 (- 47 z)}{2 \cdot 53}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.3.1.2.2.3

Rewrite the expression.

$y = \frac{14}{53} + \frac{- 47 z}{53}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$y = \frac{14}{53} + \frac{- 47 z}{53}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$y = \frac{14}{53} + \frac{- 47 z}{53}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.3.2.3.1.3

Move the negative in front of the fraction.

$y = \frac{14}{53} - \frac{47 z}{53}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$- \frac{533 - 1478 z - 822 y}{15} = 24$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4

Replace all occurrences of $y$ with $\frac{14}{53} - \frac{47 z}{53}$ in each equation.

Tap for more steps...

Step 3.4.1

Replace all occurrences of $y$ in $- \frac{533 - 1478 z - 822 y}{15} = 24$ with $\frac{14}{53} - \frac{47 z}{53}$ .

$- \frac{533 - 1478 z - 822 (\frac{14}{53} - \frac{47 z}{53})}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2

Simplify the left side.

Tap for more steps...

Step 3.4.2.1

Simplify $- \frac{533 - 1478 z - 822 (\frac{14}{53} - \frac{47 z}{53})}{15}$ .

Tap for more steps...

Step 3.4.2.1.1

Simplify the numerator.

Tap for more steps...

Step 3.4.2.1.1.1

Apply the distributive property.

$- \frac{533 - 1478 z - 822 (\frac{14}{53}) - 822 (- \frac{47 z}{53})}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.2

Multiply $- 822 (\frac{14}{53})$ .

Tap for more steps...

Step 3.4.2.1.1.2.1

Combine $- 822$ and $\frac{14}{53}$ .

$- \frac{533 - 1478 z + \frac{- 822 \cdot 14}{53} - 822 (- \frac{47 z}{53})}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.2.2

Multiply $- 822$ by $14$ .

$- \frac{533 - 1478 z + \frac{- 11508}{53} - 822 (- \frac{47 z}{53})}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{533 - 1478 z + \frac{- 11508}{53} - 822 (- \frac{47 z}{53})}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.3

Multiply $- 822 (- \frac{47 z}{53})$ .

Tap for more steps...

Step 3.4.2.1.1.3.1

Multiply $- 1$ by $- 822$ .

$- \frac{533 - 1478 z + \frac{- 11508}{53} + 822 (\frac{47 z}{53})}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.3.2

Combine $822$ and $\frac{47 z}{53}$ .

$- \frac{533 - 1478 z + \frac{- 11508}{53} + \frac{822 (47 z)}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.3.3

Multiply $47$ by $822$ .

$- \frac{533 - 1478 z + \frac{- 11508}{53} + \frac{38634 z}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{533 - 1478 z + \frac{- 11508}{53} + \frac{38634 z}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.4

Move the negative in front of the fraction.

$- \frac{533 - 1478 z - \frac{11508}{53} + \frac{38634 z}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.5

To write $533$ as a fraction with a common denominator, multiply by $\frac{53}{53}$ .

$- \frac{- 1478 z + 533 \cdot \frac{53}{53} - \frac{11508}{53} + \frac{38634 z}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.6

Combine $533$ and $\frac{53}{53}$ .

$- \frac{- 1478 z + \frac{533 \cdot 53}{53} - \frac{11508}{53} + \frac{38634 z}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.7

Combine the numerators over the common denominator.

$- \frac{- 1478 z + \frac{533 \cdot 53 - 11508}{53} + \frac{38634 z}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.8

Simplify the numerator.

Tap for more steps...

Step 3.4.2.1.1.8.1

Multiply $533$ by $53$ .

$- \frac{- 1478 z + \frac{28249 - 11508}{53} + \frac{38634 z}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.8.2

Subtract $11508$ from $28249$ .

$- \frac{- 1478 z + \frac{16741}{53} + \frac{38634 z}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{- 1478 z + \frac{16741}{53} + \frac{38634 z}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.9

To write $- 1478 z$ as a fraction with a common denominator, multiply by $\frac{53}{53}$ .

$- \frac{- 1478 z \cdot \frac{53}{53} + \frac{38634 z}{53} + \frac{16741}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.10

Combine $- 1478 z$ and $\frac{53}{53}$ .

$- \frac{\frac{- 1478 z \cdot 53}{53} + \frac{38634 z}{53} + \frac{16741}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.11

Combine the numerators over the common denominator.

$- \frac{\frac{- 1478 z \cdot 53 + 38634 z}{53} + \frac{16741}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.12

Combine the numerators over the common denominator.

$- \frac{\frac{- 1478 z \cdot 53 + 38634 z + 16741}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.13

Rewrite $\frac{- 1478 z \cdot 53 + 38634 z + 16741}{53}$ in a factored form.

Tap for more steps...

Step 3.4.2.1.1.13.1

Multiply $53$ by $- 1478$ .

$- \frac{\frac{- 78334 z + 38634 z + 16741}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.1.13.2

Add $- 78334 z$ and $38634 z$ .

$- \frac{\frac{- 39700 z + 16741}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{\frac{- 39700 z + 16741}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{\frac{- 39700 z + 16741}{53}}{15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$- (\frac{- 39700 z + 16741}{53} \cdot \frac{1}{15}) = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.3

Multiply $\frac{- 39700 z + 16741}{53} \cdot \frac{1}{15}$ .

Tap for more steps...

Step 3.4.2.1.3.1

Multiply $\frac{- 39700 z + 16741}{53}$ by $\frac{1}{15}$ .

$- \frac{- 39700 z + 16741}{53 \cdot 15} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.3.2

Multiply $53$ by $15$ .

$- \frac{- 39700 z + 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$- \frac{- 39700 z + 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.4

Factor $- 1$ out of $- 39700 z$ .

$- \frac{- (39700 z) + 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.5

Rewrite $16741$ as $- 1 (- 16741)$ .

$- \frac{- (39700 z) - 1 \cdot - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.6

Factor $- 1$ out of $- (39700 z) - 1 (- 16741)$ .

$- \frac{- (39700 z - 16741)}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.7

Simplify the expression.

Tap for more steps...

Step 3.4.2.1.7.1

Rewrite $- (39700 z - 16741)$ as $- 1 (39700 z - 16741)$ .

$- \frac{- 1 (39700 z - 16741)}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.7.2

Move the negative in front of the fraction.

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.7.3

Multiply $- 1$ by $- 1$ .

$1 (\frac{39700 z - 16741}{795}) = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.2.1.7.4

Multiply $\frac{39700 z - 16741}{795}$ by $1$ .

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$

Step 3.4.3

Replace all occurrences of $y$ in $x = - \frac{13}{15} + \frac{9 y}{5} + \frac{28 z}{15}$ with $\frac{14}{53} - \frac{47 z}{53}$ .

$x = - \frac{13}{15} + \frac{9 (\frac{14}{53} - \frac{47 z}{53})}{5} + \frac{28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4

Simplify the right side.

Tap for more steps...

Step 3.4.4.1

Simplify $- \frac{13}{15} + \frac{9 (\frac{14}{53} - \frac{47 z}{53})}{5} + \frac{28 z}{15}$ .

Tap for more steps...

Step 3.4.4.1.1

Find the common denominator.

Tap for more steps...

Step 3.4.4.1.1.1

Multiply $\frac{9 (\frac{14}{53} - \frac{47 z}{53})}{5}$ by $\frac{3}{3}$ .

$x = - \frac{13}{15} + \frac{9 (\frac{14}{53} - \frac{47 z}{53})}{5} \cdot \frac{3}{3} + \frac{28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.1.2

Multiply $\frac{9 (\frac{14}{53} - \frac{47 z}{53})}{5}$ by $\frac{3}{3}$ .

$x = - \frac{13}{15} + \frac{9 (\frac{14}{53} - \frac{47 z}{53}) \cdot 3}{5 \cdot 3} + \frac{28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.1.3

Reorder the factors of $5 \cdot 3$ .

$x = - \frac{13}{15} + \frac{9 (\frac{14}{53} - \frac{47 z}{53}) \cdot 3}{3 \cdot 5} + \frac{28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.1.4

Multiply $3$ by $5$ .

$x = - \frac{13}{15} + \frac{9 (\frac{14}{53} - \frac{47 z}{53}) \cdot 3}{15} + \frac{28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{13}{15} + \frac{9 (\frac{14}{53} - \frac{47 z}{53}) \cdot 3}{15} + \frac{28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.2

Combine the numerators over the common denominator.

$x = \frac{- 13 + 9 (\frac{14}{53} - \frac{47 z}{53}) \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3

Simplify each term.

Tap for more steps...

Step 3.4.4.1.3.1

Apply the distributive property.

$x = \frac{- 13 + (9 (\frac{14}{53}) + 9 (- \frac{47 z}{53})) \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.2

Multiply $9 (\frac{14}{53})$ .

Tap for more steps...

Step 3.4.4.1.3.2.1

Combine $9$ and $\frac{14}{53}$ .

$x = \frac{- 13 + (\frac{9 \cdot 14}{53} + 9 (- \frac{47 z}{53})) \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.2.2

Multiply $9$ by $14$ .

$x = \frac{- 13 + (\frac{126}{53} + 9 (- \frac{47 z}{53})) \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = \frac{- 13 + (\frac{126}{53} + 9 (- \frac{47 z}{53})) \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.3

Multiply $9 (- \frac{47 z}{53})$ .

Tap for more steps...

Step 3.4.4.1.3.3.1

Multiply $- 1$ by $9$ .

$x = \frac{- 13 + (\frac{126}{53} - 9 \frac{47 z}{53}) \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.3.2

Combine $- 9$ and $\frac{47 z}{53}$ .

$x = \frac{- 13 + (\frac{126}{53} + \frac{- 9 (47 z)}{53}) \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.3.3

Multiply $47$ by $- 9$ .

$x = \frac{- 13 + (\frac{126}{53} + \frac{- 423 z}{53}) \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = \frac{- 13 + (\frac{126}{53} + \frac{- 423 z}{53}) \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.4

Move the negative in front of the fraction.

$x = \frac{- 13 + (\frac{126}{53} - \frac{423 z}{53}) \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.5

Apply the distributive property.

$x = \frac{- 13 + \frac{126}{53} \cdot 3 - \frac{423 z}{53} \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.6

Multiply $\frac{126}{53} \cdot 3$ .

Tap for more steps...

Step 3.4.4.1.3.6.1

Combine $\frac{126}{53}$ and $3$ .

$x = \frac{- 13 + \frac{126 \cdot 3}{53} - \frac{423 z}{53} \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.6.2

Multiply $126$ by $3$ .

$x = \frac{- 13 + \frac{378}{53} - \frac{423 z}{53} \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = \frac{- 13 + \frac{378}{53} - \frac{423 z}{53} \cdot 3 + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.7

Multiply $- \frac{423 z}{53} \cdot 3$ .

Tap for more steps...

Step 3.4.4.1.3.7.1

Multiply $3$ by $- 1$ .

$x = \frac{- 13 + \frac{378}{53} - 3 \frac{423 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.7.2

Combine $- 3$ and $\frac{423 z}{53}$ .

$x = \frac{- 13 + \frac{378}{53} + \frac{- 3 (423 z)}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.7.3

Multiply $423$ by $- 3$ .

$x = \frac{- 13 + \frac{378}{53} + \frac{- 1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = \frac{- 13 + \frac{378}{53} + \frac{- 1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.3.8

Move the negative in front of the fraction.

$x = \frac{- 13 + \frac{378}{53} - \frac{1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = \frac{- 13 + \frac{378}{53} - \frac{1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.4

To write $- 13$ as a fraction with a common denominator, multiply by $\frac{53}{53}$ .

$x = \frac{- 13 \cdot \frac{53}{53} + \frac{378}{53} - \frac{1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.5

Combine $- 13$ and $\frac{53}{53}$ .

$x = \frac{\frac{- 13 \cdot 53}{53} + \frac{378}{53} - \frac{1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.6

Combine the numerators over the common denominator.

$x = \frac{\frac{- 13 \cdot 53 + 378}{53} - \frac{1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.7

Simplify the numerator.

Tap for more steps...

Step 3.4.4.1.7.1

Multiply $- 13$ by $53$ .

$x = \frac{\frac{- 689 + 378}{53} - \frac{1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.7.2

Add $- 689$ and $378$ .

$x = \frac{\frac{- 311}{53} - \frac{1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = \frac{\frac{- 311}{53} - \frac{1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.8

Move the negative in front of the fraction.

$x = \frac{- \frac{311}{53} - \frac{1269 z}{53} + 28 z}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.9

To write $28 z$ as a fraction with a common denominator, multiply by $\frac{53}{53}$ .

$x = \frac{- \frac{311}{53} - \frac{1269 z}{53} + 28 z \cdot \frac{53}{53}}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.10

Combine $28 z$ and $\frac{53}{53}$ .

$x = \frac{- \frac{311}{53} - \frac{1269 z}{53} + \frac{28 z \cdot 53}{53}}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.11

Combine the numerators over the common denominator.

$x = \frac{- \frac{311}{53} + \frac{- 1269 z + 28 z \cdot 53}{53}}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.12

Combine the numerators over the common denominator.

$x = \frac{\frac{- 311 - 1269 z + 28 z \cdot 53}{53}}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.13

Multiply $53$ by $28$ .

$x = \frac{\frac{- 311 - 1269 z + 1484 z}{53}}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.14

Add $- 1269 z$ and $1484 z$ .

$x = \frac{\frac{- 311 + 215 z}{53}}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.15

Rewrite $- 311$ as $- 1 (311)$ .

$x = \frac{\frac{- 1 \cdot 311 + 215 z}{53}}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.16

Factor $- 1$ out of $215 z$ .

$x = \frac{\frac{- 1 \cdot 311 - (- 215 z)}{53}}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.17

Factor $- 1$ out of $- 1 (311) - (- 215 z)$ .

$x = \frac{\frac{- 1 (311 - 215 z)}{53}}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.18

Move the negative in front of the fraction.

$x = \frac{- \frac{311 - 215 z}{53}}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.19

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{311 - 215 z}{53} \cdot \frac{1}{15}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.20

Multiply $- \frac{311 - 215 z}{53} \cdot \frac{1}{15}$ .

Tap for more steps...

Step 3.4.4.1.20.1

Multiply $\frac{1}{15}$ by $\frac{311 - 215 z}{53}$ .

$x = - \frac{311 - 215 z}{15 \cdot 53}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.4.4.1.20.2

Multiply $15$ by $53$ .

$x = - \frac{311 - 215 z}{795}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{311 - 215 z}{795}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{311 - 215 z}{795}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{311 - 215 z}{795}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{311 - 215 z}{795}$

$\frac{39700 z - 16741}{795} = 24$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.5

Solve for $z$ in $\frac{39700 z - 16741}{795} = 24$ .

Tap for more steps...

Step 3.5.1

Multiply both sides by $795$ .

$\frac{39700 z - 16741}{795} \cdot 795 = 24 \cdot 795$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.5.2

Simplify.

Tap for more steps...

Step 3.5.2.1

Simplify the left side.

Tap for more steps...

Step 3.5.2.1.1

Cancel the common factor of $795$ .

Tap for more steps...

Step 3.5.2.1.1.1

Cancel the common factor.

$\frac{39700 z - 16741}{795} \cdot 795 = 24 \cdot 795$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.5.2.1.1.2

Rewrite the expression.

$39700 z - 16741 = 24 \cdot 795$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$39700 z - 16741 = 24 \cdot 795$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$39700 z - 16741 = 24 \cdot 795$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.5.2.2

Simplify the right side.

Tap for more steps...

Step 3.5.2.2.1

Multiply $24$ by $795$ .

$39700 z - 16741 = 19080$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$39700 z - 16741 = 19080$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$39700 z - 16741 = 19080$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.5.3

Solve for $z$ .

Tap for more steps...

Step 3.5.3.1

Move all terms not containing $z$ to the right side of the equation.

Tap for more steps...

Step 3.5.3.1.1

Add $16741$ to both sides of the equation.

$39700 z = 19080 + 16741$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.5.3.1.2

Add $19080$ and $16741$ .

$39700 z = 35821$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$39700 z = 35821$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.5.3.2

Divide each term in $39700 z = 35821$ by $39700$ and simplify.

Tap for more steps...

Step 3.5.3.2.1

Divide each term in $39700 z = 35821$ by $39700$ .

$\frac{39700 z}{39700} = \frac{35821}{39700}$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.5.3.2.2

Simplify the left side.

Tap for more steps...

Step 3.5.3.2.2.1

Cancel the common factor of $39700$ .

Tap for more steps...

Step 3.5.3.2.2.1.1

Cancel the common factor.

$\frac{39700 z}{39700} = \frac{35821}{39700}$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.5.3.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{35821}{39700}$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$z = \frac{35821}{39700}$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$z = \frac{35821}{39700}$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$z = \frac{35821}{39700}$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$z = \frac{35821}{39700}$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$z = \frac{35821}{39700}$

$x = - \frac{311 - 215 z}{795}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6

Replace all occurrences of $z$ with $\frac{35821}{39700}$ in each equation.

Tap for more steps...

Step 3.6.1

Replace all occurrences of $z$ in $x = - \frac{311 - 215 z}{795}$ with $\frac{35821}{39700}$ .

$x = - \frac{311 - 215 (\frac{35821}{39700})}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2

Simplify the right side.

Tap for more steps...

Step 3.6.2.1

Simplify $- \frac{311 - 215 (\frac{35821}{39700})}{795}$ .

Tap for more steps...

Step 3.6.2.1.1

Simplify the numerator.

Tap for more steps...

Step 3.6.2.1.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.6.2.1.1.1.1

Factor $5$ out of $- 215$ .

$x = - \frac{311 + 5 (- 43) (\frac{35821}{39700})}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.1.2

Factor $5$ out of $39700$ .

$x = - \frac{311 + 5 \cdot (- 43 \frac{35821}{5 \cdot 7940})}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.1.3

Cancel the common factor.

$x = - \frac{311 + 5 \cdot (- 43 \frac{35821}{5 \cdot 7940})}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.1.4

Rewrite the expression.

$x = - \frac{311 - 43 (\frac{35821}{7940})}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{311 - 43 (\frac{35821}{7940})}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.2

Combine $- 43$ and $\frac{35821}{7940}$ .

$x = - \frac{311 + \frac{- 43 \cdot 35821}{7940}}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.3

Multiply $- 43$ by $35821$ .

$x = - \frac{311 + \frac{- 1540303}{7940}}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.4

Move the negative in front of the fraction.

$x = - \frac{311 - \frac{1540303}{7940}}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.5

To write $311$ as a fraction with a common denominator, multiply by $\frac{7940}{7940}$ .

$x = - \frac{311 \cdot \frac{7940}{7940} - \frac{1540303}{7940}}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.6

Combine $311$ and $\frac{7940}{7940}$ .

$x = - \frac{\frac{311 \cdot 7940}{7940} - \frac{1540303}{7940}}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.7

Combine the numerators over the common denominator.

$x = - \frac{\frac{311 \cdot 7940 - 1540303}{7940}}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.8

Simplify the numerator.

Tap for more steps...

Step 3.6.2.1.1.8.1

Multiply $311$ by $7940$ .

$x = - \frac{\frac{2469340 - 1540303}{7940}}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.1.8.2

Subtract $1540303$ from $2469340$ .

$x = - \frac{\frac{929037}{7940}}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{\frac{929037}{7940}}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{\frac{929037}{7940}}{795}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$x = - (\frac{929037}{7940} \cdot \frac{1}{795})$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.3

Cancel the common factor of $159$ .

Tap for more steps...

Step 3.6.2.1.3.1

Factor $159$ out of $929037$ .

$x = - (\frac{159 (5843)}{7940} \cdot \frac{1}{795})$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.3.2

Factor $159$ out of $795$ .

$x = - (\frac{159 \cdot 5843}{7940} \cdot \frac{1}{159 \cdot 5})$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.3.3

Cancel the common factor.

$x = - (\frac{159 \cdot 5843}{7940} \cdot \frac{1}{159 \cdot 5})$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.3.4

Rewrite the expression.

$x = - (\frac{5843}{7940} \cdot \frac{1}{5})$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - (\frac{5843}{7940} \cdot \frac{1}{5})$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.4

Multiply $\frac{5843}{7940}$ by $\frac{1}{5}$ .

$x = - \frac{5843}{7940 \cdot 5}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.2.1.5

Multiply $7940$ by $5$ .

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

$y = \frac{14}{53} - \frac{47 z}{53}$

Step 3.6.3

Replace all occurrences of $z$ in $y = \frac{14}{53} - \frac{47 z}{53}$ with $\frac{35821}{39700}$ .

$y = \frac{14}{53} - \frac{47 (\frac{35821}{39700})}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4

Simplify the right side.

Tap for more steps...

Step 3.6.4.1

Simplify $\frac{14}{53} - \frac{47 (\frac{35821}{39700})}{53}$ .

Tap for more steps...

Step 3.6.4.1.1

Combine the numerators over the common denominator.

$y = \frac{14 - 47 (\frac{35821}{39700})}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.2

Simplify each term.

Tap for more steps...

Step 3.6.4.1.2.1

Multiply $- 47 (\frac{35821}{39700})$ .

Tap for more steps...

Step 3.6.4.1.2.1.1

Combine $- 47$ and $\frac{35821}{39700}$ .

$y = \frac{14 + \frac{- 47 \cdot 35821}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.2.1.2

Multiply $- 47$ by $35821$ .

$y = \frac{14 + \frac{- 1683587}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

$y = \frac{14 + \frac{- 1683587}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.2.2

Move the negative in front of the fraction.

$y = \frac{14 - \frac{1683587}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

$y = \frac{14 - \frac{1683587}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.3

To write $14$ as a fraction with a common denominator, multiply by $\frac{39700}{39700}$ .

$y = \frac{14 \cdot \frac{39700}{39700} - \frac{1683587}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.4

Combine $14$ and $\frac{39700}{39700}$ .

$y = \frac{\frac{14 \cdot 39700}{39700} - \frac{1683587}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.5

Combine the numerators over the common denominator.

$y = \frac{\frac{14 \cdot 39700 - 1683587}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.6

Simplify the numerator.

Tap for more steps...

Step 3.6.4.1.6.1

Multiply $14$ by $39700$ .

$y = \frac{\frac{555800 - 1683587}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.6.2

Subtract $1683587$ from $555800$ .

$y = \frac{\frac{- 1127787}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

$y = \frac{\frac{- 1127787}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.7

Move the negative in front of the fraction.

$y = \frac{- \frac{1127787}{39700}}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.8

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{1127787}{39700} \cdot \frac{1}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.9

Cancel the common factor of $53$ .

Tap for more steps...

Step 3.6.4.1.9.1

Move the leading negative in $- \frac{1127787}{39700}$ into the numerator.

$y = \frac{- 1127787}{39700} \cdot \frac{1}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.9.2

Factor $53$ out of $- 1127787$ .

$y = \frac{53 (- 21279)}{39700} \cdot \frac{1}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.9.3

Cancel the common factor.

$y = \frac{53 \cdot - 21279}{39700} \cdot \frac{1}{53}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.9.4

Rewrite the expression.

$y = \frac{- 21279}{39700}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

$y = \frac{- 21279}{39700}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.6.4.1.10

Move the negative in front of the fraction.

$y = - \frac{21279}{39700}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

$y = - \frac{21279}{39700}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

$y = - \frac{21279}{39700}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

$y = - \frac{21279}{39700}$

$x = - \frac{5843}{39700}$

$z = \frac{35821}{39700}$

Step 3.7

List all of the solutions.

$y = - \frac{21279}{39700}, x = - \frac{5843}{39700}, z = \frac{35821}{39700}$