Finite Math Examples

$2 x + 5 y - 2 z = 14$ , $5 x - 6 y + 2 z = 0$ , $4 x - y + 3 z = - 7$

Step 1

Solve for $x$ in $2 x + 5 y - 2 z = 14$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Subtract $5 y$ from both sides of the equation.

$2 x - 2 z = 14 - 5 y$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

Step 1.1.2

Add $2 z$ to both sides of the equation.

$2 x = 14 - 5 y + 2 z$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

$2 x = 14 - 5 y + 2 z$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

Step 1.2

Divide each term in $2 x = 14 - 5 y + 2 z$ by $2$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $2 x = 14 - 5 y + 2 z$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2} + \frac{- 5 y}{2} + \frac{2 z}{2}$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2} + \frac{- 5 y}{2} + \frac{2 z}{2}$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{14}{2} + \frac{- 5 y}{2} + \frac{2 z}{2}$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

$x = \frac{14}{2} + \frac{- 5 y}{2} + \frac{2 z}{2}$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

$x = \frac{14}{2} + \frac{- 5 y}{2} + \frac{2 z}{2}$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Divide $14$ by $2$ .

$x = 7 + \frac{- 5 y}{2} + \frac{2 z}{2}$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$x = 7 - \frac{5 y}{2} + \frac{2 z}{2}$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

Step 1.2.3.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.3.1.3.1

Cancel the common factor.

$x = 7 - \frac{5 y}{2} + \frac{2 z}{2}$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

Step 1.2.3.1.3.2

Divide $z$ by $1$ .

$x = 7 - \frac{5 y}{2} + z$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

$x = 7 - \frac{5 y}{2} + z$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

$x = 7 - \frac{5 y}{2} + z$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

$x = 7 - \frac{5 y}{2} + z$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

$x = 7 - \frac{5 y}{2} + z$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

$x = 7 - \frac{5 y}{2} + z$

$5 x - 6 y + 2 z = 0$

$4 x - y + 3 z = - 7$

Step 2

Replace all occurrences of $x$ with $7 - \frac{5 y}{2} + z$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $5 x - 6 y + 2 z = 0$ with $7 - \frac{5 y}{2} + z$ .

$5 (7 - \frac{5 y}{2} + z) - 6 y + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $5 (7 - \frac{5 y}{2} + z) - 6 y + 2 z$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$5 \cdot 7 + 5 (- \frac{5 y}{2}) + 5 z - 6 y + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.1.2

Simplify.

Tap for more steps...

Step 2.2.1.1.2.1

Multiply $5$ by $7$ .

$35 + 5 (- \frac{5 y}{2}) + 5 z - 6 y + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.1.2.2

Multiply $5 (- \frac{5 y}{2})$ .

Tap for more steps...

Step 2.2.1.1.2.2.1

Multiply $- 1$ by $5$ .

$35 - 5 \frac{5 y}{2} + 5 z - 6 y + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.1.2.2.2

Combine $- 5$ and $\frac{5 y}{2}$ .

$35 + \frac{- 5 (5 y)}{2} + 5 z - 6 y + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.1.2.2.3

Multiply $5$ by $- 5$ .

$35 + \frac{- 25 y}{2} + 5 z - 6 y + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

$35 + \frac{- 25 y}{2} + 5 z - 6 y + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

$35 + \frac{- 25 y}{2} + 5 z - 6 y + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.1.3

Move the negative in front of the fraction.

$35 - \frac{25 y}{2} + 5 z - 6 y + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

$35 - \frac{25 y}{2} + 5 z - 6 y + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.2

To write $- 6 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$35 + 5 z - \frac{25 y}{2} - 6 y \cdot \frac{2}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.3

Simplify terms.

Tap for more steps...

Step 2.2.1.3.1

Combine $- 6 y$ and $\frac{2}{2}$ .

$35 + 5 z - \frac{25 y}{2} + \frac{- 6 y \cdot 2}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$35 + 5 z + \frac{- 25 y - 6 y \cdot 2}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

$35 + 5 z + \frac{- 25 y - 6 y \cdot 2}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.4

Simplify each term.

Tap for more steps...

Step 2.2.1.4.1

Simplify the numerator.

Tap for more steps...

Step 2.2.1.4.1.1

Factor $y$ out of $- 25 y - 6 y \cdot 2$ .

Tap for more steps...

Step 2.2.1.4.1.1.1

Factor $y$ out of $- 25 y$ .

$35 + 5 z + \frac{y \cdot - 25 - 6 y \cdot 2}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.4.1.1.2

Factor $y$ out of $- 6 y \cdot 2$ .

$35 + 5 z + \frac{y \cdot - 25 + y (- 6 \cdot 2)}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.4.1.1.3

Factor $y$ out of $y \cdot - 25 + y (- 6 \cdot 2)$ .

$35 + 5 z + \frac{y (- 25 - 6 \cdot 2)}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

$35 + 5 z + \frac{y (- 25 - 6 \cdot 2)}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.4.1.2

Multiply $- 6$ by $2$ .

$35 + 5 z + \frac{y (- 25 - 12)}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.4.1.3

Subtract $12$ from $- 25$ .

$35 + 5 z + \frac{y \cdot - 37}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

$35 + 5 z + \frac{y \cdot - 37}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.4.2

Move $- 37$ to the left of $y$ .

$35 + 5 z + \frac{- 37 \cdot y}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.4.3

Move the negative in front of the fraction.

$35 + 5 z - \frac{37 y}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

$35 + 5 z - \frac{37 y}{2} + 2 z = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.2.1.5

Add $5 z$ and $2 z$ .

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$4 x - y + 3 z = - 7$

Step 2.3

Replace all occurrences of $x$ in $4 x - y + 3 z = - 7$ with $7 - \frac{5 y}{2} + z$ .

$4 (7 - \frac{5 y}{2} + z) - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $4 (7 - \frac{5 y}{2} + z) - y + 3 z$ .

Tap for more steps...

Step 2.4.1.1

Simplify each term.

Tap for more steps...

Step 2.4.1.1.1

Apply the distributive property.

$4 \cdot 7 + 4 (- \frac{5 y}{2}) + 4 z - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 2.4.1.1.2

Simplify.

Tap for more steps...

Step 2.4.1.1.2.1

Multiply $4$ by $7$ .

$28 + 4 (- \frac{5 y}{2}) + 4 z - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 2.4.1.1.2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.1.1.2.2.1

Move the leading negative in $- \frac{5 y}{2}$ into the numerator.

$28 + 4 (\frac{- 5 y}{2}) + 4 z - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 2.4.1.1.2.2.2

Factor $2$ out of $4$ .

$28 + 2 (2) (\frac{- 5 y}{2}) + 4 z - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 2.4.1.1.2.2.3

Cancel the common factor.

$28 + 2 \cdot (2 (\frac{- 5 y}{2})) + 4 z - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 2.4.1.1.2.2.4

Rewrite the expression.

$28 + 2 (- 5 y) + 4 z - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$28 + 2 (- 5 y) + 4 z - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 2.4.1.1.2.3

Multiply $- 5$ by $2$ .

$28 - 10 y + 4 z - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$28 - 10 y + 4 z - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$28 - 10 y + 4 z - y + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 2.4.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.4.1.2.1

Subtract $y$ from $- 10 y$ .

$28 - 11 y + 4 z + 3 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 2.4.1.2.2

Add $4 z$ and $3 z$ .

$28 - 11 y + 7 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$28 - 11 y + 7 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$28 - 11 y + 7 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$28 - 11 y + 7 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$28 - 11 y + 7 z = - 7$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 3

Solve for $y$ in $28 - 11 y + 7 z = - 7$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $28$ from both sides of the equation.

$- 11 y + 7 z = - 7 - 28$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 3.1.2

Subtract $7 z$ from both sides of the equation.

$- 11 y = - 7 - 28 - 7 z$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 3.1.3

Subtract $28$ from $- 7$ .

$- 11 y = - 35 - 7 z$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$- 11 y = - 35 - 7 z$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 3.2

Divide each term in $- 11 y = - 35 - 7 z$ by $- 11$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 11 y = - 35 - 7 z$ by $- 11$ .

$\frac{- 11 y}{- 11} = \frac{- 35}{- 11} + \frac{- 7 z}{- 11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 11$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 11 y}{- 11} = \frac{- 35}{- 11} + \frac{- 7 z}{- 11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 35}{- 11} + \frac{- 7 z}{- 11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$y = \frac{- 35}{- 11} + \frac{- 7 z}{- 11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$y = \frac{- 35}{- 11} + \frac{- 7 z}{- 11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Simplify each term.

Tap for more steps...

Step 3.2.3.1.1

Dividing two negative values results in a positive value.

$y = \frac{35}{11} + \frac{- 7 z}{- 11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 3.2.3.1.2

Dividing two negative values results in a positive value.

$y = \frac{35}{11} + \frac{7 z}{11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$y = \frac{35}{11} + \frac{7 z}{11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$y = \frac{35}{11} + \frac{7 z}{11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$y = \frac{35}{11} + \frac{7 z}{11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

$y = \frac{35}{11} + \frac{7 z}{11}$

$35 + 7 z - \frac{37 y}{2} = 0$

$x = 7 - \frac{5 y}{2} + z$

Step 4

Replace all occurrences of $y$ with $\frac{35}{11} + \frac{7 z}{11}$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $35 + 7 z - \frac{37 y}{2} = 0$ with $\frac{35}{11} + \frac{7 z}{11}$ .

$35 + 7 z - \frac{37 (\frac{35}{11} + \frac{7 z}{11})}{2} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Simplify $35 + 7 z - \frac{37 (\frac{35}{11} + \frac{7 z}{11})}{2}$ .

Tap for more steps...

Step 4.2.1.1

Simplify each term.

Tap for more steps...

Step 4.2.1.1.1

Simplify the numerator.

Tap for more steps...

Step 4.2.1.1.1.1

Combine the numerators over the common denominator.

$35 + 7 z - \frac{37 (\frac{35 + 7 z}{11})}{2} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.1.1.2

Factor $7$ out of $35 + 7 z$ .

Tap for more steps...

Step 4.2.1.1.1.2.1

Factor $7$ out of $35$ .

$35 + 7 z - \frac{37 (\frac{7 \cdot 5 + 7 z}{11})}{2} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.1.1.2.2

Factor $7$ out of $7 \cdot 5 + 7 z$ .

$35 + 7 z - \frac{37 (\frac{7 (5 + z)}{11})}{2} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$35 + 7 z - \frac{37 (\frac{7 (5 + z)}{11})}{2} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$35 + 7 z - \frac{37 (\frac{7 (5 + z)}{11})}{2} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.1.2

Combine $37$ and $\frac{7 (5 + z)}{11}$ .

$35 + 7 z - \frac{\frac{37 (7 (5 + z))}{11}}{2} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.1.3

Multiply $37$ by $7$ .

$35 + 7 z - \frac{\frac{259 (5 + z)}{11}}{2} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.1.4

Multiply the numerator by the reciprocal of the denominator.

$35 + 7 z - (\frac{259 (5 + z)}{11} \cdot \frac{1}{2}) = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.1.5

Multiply $\frac{259 (5 + z)}{11} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 4.2.1.1.5.1

Multiply $\frac{259 (5 + z)}{11}$ by $\frac{1}{2}$ .

$35 + 7 z - \frac{259 (5 + z)}{11 \cdot 2} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.1.5.2

Multiply $11$ by $2$ .

$35 + 7 z - \frac{259 (5 + z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$35 + 7 z - \frac{259 (5 + z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$35 + 7 z - \frac{259 (5 + z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.2

To write $35$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$7 z + 35 \cdot \frac{22}{22} - \frac{259 (5 + z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.3

Simplify terms.

Tap for more steps...

Step 4.2.1.3.1

Combine $35$ and $\frac{22}{22}$ .

$7 z + \frac{35 \cdot 22}{22} - \frac{259 (5 + z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.3.2

Combine the numerators over the common denominator.

$7 z + \frac{35 \cdot 22 - 259 (5 + z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.3.3

Multiply $35$ by $22$ .

$7 z + \frac{770 - 259 (5 + z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$7 z + \frac{770 - 259 (5 + z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.4

Simplify the numerator.

Tap for more steps...

Step 4.2.1.4.1

Factor $7$ out of $770 - 259 (5 + z)$ .

Tap for more steps...

Step 4.2.1.4.1.1

Factor $7$ out of $770$ .

$7 z + \frac{7 (110) - 259 (5 + z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.4.1.2

Factor $7$ out of $- 259 (5 + z)$ .

$7 z + \frac{7 (110) + 7 (- 37 (5 + z))}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.4.1.3

Factor $7$ out of $7 (110) + 7 (- 37 (5 + z))$ .

$7 z + \frac{7 (110 - 37 (5 + z))}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$7 z + \frac{7 (110 - 37 (5 + z))}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.4.2

Apply the distributive property.

$7 z + \frac{7 (110 - 37 \cdot 5 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.4.3

Multiply $- 37$ by $5$ .

$7 z + \frac{7 (110 - 185 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.4.4

Subtract $185$ from $110$ .

$7 z + \frac{7 (- 75 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$7 z + \frac{7 (- 75 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.5

To write $7 z$ as a fraction with a common denominator, multiply by $\frac{22}{22}$ .

$7 z \cdot \frac{22}{22} + \frac{7 (- 75 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.6

Simplify terms.

Tap for more steps...

Step 4.2.1.6.1

Combine $7 z$ and $\frac{22}{22}$ .

$\frac{7 z \cdot 22}{22} + \frac{7 (- 75 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.6.2

Combine the numerators over the common denominator.

$\frac{7 z \cdot 22 + 7 (- 75 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$\frac{7 z \cdot 22 + 7 (- 75 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.7

Simplify the numerator.

Tap for more steps...

Step 4.2.1.7.1

Factor $7$ out of $7 z \cdot 22 + 7 (- 75 - 37 z)$ .

Tap for more steps...

Step 4.2.1.7.1.1

Factor $7$ out of $7 z \cdot 22$ .

$\frac{7 (z \cdot 22) + 7 (- 75 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.7.1.2

Factor $7$ out of $7 (z \cdot 22) + 7 (- 75 - 37 z)$ .

$\frac{7 (z \cdot 22 - 75 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$\frac{7 (z \cdot 22 - 75 - 37 z)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.7.2

Subtract $37 z$ from $z \cdot 22$ .

Tap for more steps...

Step 4.2.1.7.2.1

Reorder $z$ and $22$ .

$\frac{7 (22 \cdot z - 37 z - 75)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.7.2.2

Subtract $37 z$ from $22 \cdot z$ .

$\frac{7 (- 15 \cdot z - 75)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$\frac{7 (- 15 \cdot z - 75)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.7.3

Factor $15$ out of $- 15 \cdot z - 75$ .

Tap for more steps...

Step 4.2.1.7.3.1

Factor $15$ out of $- 15 \cdot z$ .

$\frac{7 (15 (- z) - 75)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.7.3.2

Factor $15$ out of $- 75$ .

$\frac{7 (15 (- z) + 15 (- 5))}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.7.3.3

Factor $15$ out of $15 (- z) + 15 (- 5)$ .

$\frac{7 (15 (- z - 5))}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$\frac{7 \cdot (15 (- z - 5))}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.7.4

Multiply $7$ by $15$ .

$\frac{105 (- z - 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$\frac{105 (- z - 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.8

Simplify with factoring out.

Tap for more steps...

Step 4.2.1.8.1

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

$\frac{105 (- (z) - 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.8.2

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{105 (- (z) - 1 \cdot 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.8.3

Factor $- 1$ out of $- (z) - 1 (5)$ .

$\frac{105 (- (z + 5))}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.8.4

Simplify the expression.

Tap for more steps...

Step 4.2.1.8.4.1

Rewrite $- (z + 5)$ as $- 1 (z + 5)$ .

$\frac{105 (- 1 (z + 5))}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.2.1.8.4.2

Move the negative in front of the fraction.

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 7 - \frac{5 y}{2} + z$

Step 4.3

Replace all occurrences of $y$ in $x = 7 - \frac{5 y}{2} + z$ with $\frac{35}{11} + \frac{7 z}{11}$ .

$x = 7 - \frac{5 (\frac{35}{11} + \frac{7 z}{11})}{2} + z$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4

Simplify the right side.

Tap for more steps...

Step 4.4.1

Simplify $7 - \frac{5 (\frac{35}{11} + \frac{7 z}{11})}{2} + z$ .

Tap for more steps...

Step 4.4.1.1

Find the common denominator.

Tap for more steps...

Step 4.4.1.1.1

Write $7$ as a fraction with denominator $1$ .

$x = \frac{7}{1} - \frac{5 (\frac{35}{11} + \frac{7 z}{11})}{2} + z$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.1.2

Multiply $\frac{7}{1}$ by $\frac{2}{2}$ .

$x = \frac{7}{1} \cdot \frac{2}{2} - \frac{5 (\frac{35}{11} + \frac{7 z}{11})}{2} + z$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.1.3

Multiply $\frac{7}{1}$ by $\frac{2}{2}$ .

$x = \frac{7 \cdot 2}{2} - \frac{5 (\frac{35}{11} + \frac{7 z}{11})}{2} + z$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.1.4

Write $z$ as a fraction with denominator $1$ .

$x = \frac{7 \cdot 2}{2} - \frac{5 (\frac{35}{11} + \frac{7 z}{11})}{2} + \frac{z}{1}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.1.5

Multiply $\frac{z}{1}$ by $\frac{2}{2}$ .

$x = \frac{7 \cdot 2}{2} - \frac{5 (\frac{35}{11} + \frac{7 z}{11})}{2} + \frac{z}{1} \cdot \frac{2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.1.6

Multiply $\frac{z}{1}$ by $\frac{2}{2}$ .

$x = \frac{7 \cdot 2}{2} - \frac{5 (\frac{35}{11} + \frac{7 z}{11})}{2} + \frac{z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = \frac{7 \cdot 2}{2} - \frac{5 (\frac{35}{11} + \frac{7 z}{11})}{2} + \frac{z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.2

Combine the numerators over the common denominator.

$x = \frac{7 \cdot 2 - 5 (\frac{35}{11} + \frac{7 z}{11}) + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.3

Simplify each term.

Tap for more steps...

Step 4.4.1.3.1

Multiply $7$ by $2$ .

$x = \frac{14 - 5 (\frac{35}{11} + \frac{7 z}{11}) + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.3.2

Apply the distributive property.

$x = \frac{14 - 5 (\frac{35}{11}) - 5 \frac{7 z}{11} + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.3.3

Multiply $- 5 (\frac{35}{11})$ .

Tap for more steps...

Step 4.4.1.3.3.1

Combine $- 5$ and $\frac{35}{11}$ .

$x = \frac{14 + \frac{- 5 \cdot 35}{11} - 5 \frac{7 z}{11} + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.3.3.2

Multiply $- 5$ by $35$ .

$x = \frac{14 + \frac{- 175}{11} - 5 \frac{7 z}{11} + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = \frac{14 + \frac{- 175}{11} - 5 \frac{7 z}{11} + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.3.4

Multiply $- 5 \frac{7 z}{11}$ .

Tap for more steps...

Step 4.4.1.3.4.1

Combine $- 5$ and $\frac{7 z}{11}$ .

$x = \frac{14 + \frac{- 175}{11} + \frac{- 5 (7 z)}{11} + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.3.4.2

Multiply $7$ by $- 5$ .

$x = \frac{14 + \frac{- 175}{11} + \frac{- 35 z}{11} + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = \frac{14 + \frac{- 175}{11} + \frac{- 35 z}{11} + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.3.5

Simplify each term.

Tap for more steps...

Step 4.4.1.3.5.1

Move the negative in front of the fraction.

$x = \frac{14 - \frac{175}{11} + \frac{- 35 z}{11} + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.3.5.2

Move the negative in front of the fraction.

$x = \frac{14 - \frac{175}{11} - \frac{35 z}{11} + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = \frac{14 - \frac{175}{11} - \frac{35 z}{11} + z \cdot 2}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.3.6

Move $2$ to the left of $z$ .

$x = \frac{14 - \frac{175}{11} - \frac{35 z}{11} + 2 z}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = \frac{14 - \frac{175}{11} - \frac{35 z}{11} + 2 z}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.4

To write $14$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x = \frac{14 \cdot \frac{11}{11} - \frac{175}{11} - \frac{35 z}{11} + 2 z}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.5

Combine $14$ and $\frac{11}{11}$ .

$x = \frac{\frac{14 \cdot 11}{11} - \frac{175}{11} - \frac{35 z}{11} + 2 z}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.6

Combine the numerators over the common denominator.

$x = \frac{\frac{14 \cdot 11 - 175}{11} - \frac{35 z}{11} + 2 z}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.7

Simplify the numerator.

Tap for more steps...

Step 4.4.1.7.1

Multiply $14$ by $11$ .

$x = \frac{\frac{154 - 175}{11} - \frac{35 z}{11} + 2 z}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.7.2

Subtract $175$ from $154$ .

$x = \frac{\frac{- 21}{11} - \frac{35 z}{11} + 2 z}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = \frac{\frac{- 21}{11} - \frac{35 z}{11} + 2 z}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.8

Move the negative in front of the fraction.

$x = \frac{- \frac{21}{11} - \frac{35 z}{11} + 2 z}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.9

To write $2 z$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x = \frac{- \frac{21}{11} - \frac{35 z}{11} + 2 z \cdot \frac{11}{11}}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.10

Combine $2 z$ and $\frac{11}{11}$ .

$x = \frac{- \frac{21}{11} - \frac{35 z}{11} + \frac{2 z \cdot 11}{11}}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.11

Combine the numerators over the common denominator.

$x = \frac{- \frac{21}{11} + \frac{- 35 z + 2 z \cdot 11}{11}}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.12

Combine the numerators over the common denominator.

$x = \frac{\frac{- 21 - 35 z + 2 z \cdot 11}{11}}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.13

Multiply $11$ by $2$ .

$x = \frac{\frac{- 21 - 35 z + 22 z}{11}}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.14

Add $- 35 z$ and $22 z$ .

$x = \frac{\frac{- 21 - 13 z}{11}}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.15

Rewrite $- 21$ as $- 1 (21)$ .

$x = \frac{\frac{- 1 \cdot 21 - 13 z}{11}}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.16

Factor $- 1$ out of $- 13 z$ .

$x = \frac{\frac{- 1 \cdot 21 - (13 z)}{11}}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.17

Factor $- 1$ out of $- 1 (21) - (13 z)$ .

$x = \frac{\frac{- 1 (21 + 13 z)}{11}}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.18

Move the negative in front of the fraction.

$x = \frac{- \frac{21 + 13 z}{11}}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.19

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{21 + 13 z}{11} \cdot \frac{1}{2}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.20

Multiply $- \frac{21 + 13 z}{11} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 4.4.1.20.1

Multiply $\frac{1}{2}$ by $\frac{21 + 13 z}{11}$ .

$x = - \frac{21 + 13 z}{2 \cdot 11}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 4.4.1.20.2

Multiply $2$ by $11$ .

$x = - \frac{21 + 13 z}{22}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = - \frac{21 + 13 z}{22}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = - \frac{21 + 13 z}{22}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = - \frac{21 + 13 z}{22}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = - \frac{21 + 13 z}{22}$

$- \frac{105 (z + 5)}{22} = 0$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 5

Solve for $z$ in $- \frac{105 (z + 5)}{22} = 0$ .

Tap for more steps...

Step 5.1

Set the numerator equal to zero.

$105 (z + 5) = 0$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 5.2

Solve the equation for $z$ .

Tap for more steps...

Step 5.2.1

Divide each term in $105 (z + 5) = 0$ by $105$ and simplify.

Tap for more steps...

Step 5.2.1.1

Divide each term in $105 (z + 5) = 0$ by $105$ .

$\frac{105 (z + 5)}{105} = \frac{0}{105}$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 5.2.1.2

Simplify the left side.

Tap for more steps...

Step 5.2.1.2.1

Cancel the common factor of $105$ .

Tap for more steps...

Step 5.2.1.2.1.1

Cancel the common factor.

$\frac{105 (z + 5)}{105} = \frac{0}{105}$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 5.2.1.2.1.2

Divide $z + 5$ by $1$ .

$z + 5 = \frac{0}{105}$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

$z + 5 = \frac{0}{105}$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

$z + 5 = \frac{0}{105}$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 5.2.1.3

Simplify the right side.

Tap for more steps...

Step 5.2.1.3.1

Divide $0$ by $105$ .

$z + 5 = 0$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

$z + 5 = 0$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

$z + 5 = 0$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 5.2.2

Subtract $5$ from both sides of the equation.

$z = - 5$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

$z = - 5$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

$z = - 5$

$x = - \frac{21 + 13 z}{22}$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 6

Replace all occurrences of $z$ with $- 5$ in each equation.

Tap for more steps...

Step 6.1

Replace all occurrences of $z$ in $x = - \frac{21 + 13 z}{22}$ with $- 5$ .

$x = - \frac{21 + 13 (- 5)}{22}$

$z = - 5$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify $- \frac{21 + 13 (- 5)}{22}$ .

Tap for more steps...

Step 6.2.1.1

Simplify the numerator.

Tap for more steps...

Step 6.2.1.1.1

Multiply $13$ by $- 5$ .

$x = - \frac{21 - 65}{22}$

$z = - 5$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 6.2.1.1.2

Subtract $65$ from $21$ .

$x = - \frac{- 44}{22}$

$z = - 5$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = - \frac{- 44}{22}$

$z = - 5$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 6.2.1.2

Simplify the expression.

Tap for more steps...

Step 6.2.1.2.1

Divide $- 44$ by $22$ .

$x = 2$

$z = - 5$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 6.2.1.2.2

Multiply $- 1$ by $- 2$ .

$x = 2$

$z = - 5$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 2$

$z = - 5$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 2$

$z = - 5$

$y = \frac{35}{11} + \frac{7 z}{11}$

$x = 2$

$z = - 5$

$y = \frac{35}{11} + \frac{7 z}{11}$

Step 6.3

Replace all occurrences of $z$ in $y = \frac{35}{11} + \frac{7 z}{11}$ with $- 5$ .

$y = \frac{35}{11} + \frac{7 (- 5)}{11}$

$x = 2$

$z = - 5$

Step 6.4

Simplify the right side.

Tap for more steps...

Step 6.4.1

Simplify $\frac{35}{11} + \frac{7 (- 5)}{11}$ .

Tap for more steps...

Step 6.4.1.1

Combine the numerators over the common denominator.

$y = \frac{35 + 7 (- 5)}{11}$

$x = 2$

$z = - 5$

Step 6.4.1.2

Simplify the expression.

Tap for more steps...

Step 6.4.1.2.1

Multiply $7$ by $- 5$ .

$y = \frac{35 - 35}{11}$

$x = 2$

$z = - 5$

Step 6.4.1.2.2

Subtract $35$ from $35$ .

$y = \frac{0}{11}$

$x = 2$

$z = - 5$

Step 6.4.1.2.3

Divide $0$ by $11$ .

$y = 0$

$x = 2$

$z = - 5$

$y = 0$

$x = 2$

$z = - 5$

$y = 0$

$x = 2$

$z = - 5$

$y = 0$

$x = 2$

$z = - 5$

$y = 0$

$x = 2$

$z = - 5$

Step 7

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(2, 0, - 5)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(2, 0, - 5)$

Equation Form:

$x = 2, y = 0, z = - 5$