Precalculus Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Subtract $2 y$ from both sides of the equation.

$x + z = 7 - 2 y$

$x - 2 y - 4 z = 0$

$2 x - y + 4 z = - 3$

Step 1.2

Subtract $z$ from both sides of the equation.

$x = 7 - 2 y - z$

$x - 2 y - 4 z = 0$

$2 x - y + 4 z = - 3$

$x = 7 - 2 y - z$

$x - 2 y - 4 z = 0$

$2 x - y + 4 z = - 3$

Step 2

Replace all occurrences of $x$ with $7 - 2 y - z$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $x - 2 y - 4 z = 0$ with $7 - 2 y - z$ .

$(7 - 2 y - z) - 2 y - 4 z = 0$

$x = 7 - 2 y - z$

$2 x - y + 4 z = - 3$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $(7 - 2 y - z) - 2 y - 4 z$ .

Tap for more steps...

Step 2.2.1.1

Subtract $2 y$ from $- 2 y$ .

$7 - 4 y - z - 4 z = 0$

$x = 7 - 2 y - z$

$2 x - y + 4 z = - 3$

Step 2.2.1.2

Subtract $4 z$ from $- z$ .

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$2 x - y + 4 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$2 x - y + 4 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$2 x - y + 4 z = - 3$

Step 2.3

Replace all occurrences of $x$ in $2 x - y + 4 z = - 3$ with $7 - 2 y - z$ .

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

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $2 (7 - 2 y - z) - y + 4 z$ .

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.

$2 \cdot 7 + 2 (- 2 y) + 2 (- z) - y + 4 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 2.4.1.1.2

Simplify.

Tap for more steps...

Step 2.4.1.1.2.1

Multiply $2$ by $7$ .

$14 + 2 (- 2 y) + 2 (- z) - y + 4 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 2.4.1.1.2.2

Multiply $- 2$ by $2$ .

$14 - 4 y + 2 (- z) - y + 4 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 2.4.1.1.2.3

Multiply $- 1$ by $2$ .

$14 - 4 y - 2 z - y + 4 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$14 - 4 y - 2 z - y + 4 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$14 - 4 y - 2 z - y + 4 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 2.4.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.4.1.2.1

Subtract $y$ from $- 4 y$ .

$14 - 5 y - 2 z + 4 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 2.4.1.2.2

Add $- 2 z$ and $4 z$ .

$14 - 5 y + 2 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$14 - 5 y + 2 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$14 - 5 y + 2 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$14 - 5 y + 2 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$14 - 5 y + 2 z = - 3$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 3

Solve for $y$ in $14 - 5 y + 2 z = - 3$ .

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 $14$ from both sides of the equation.

$- 5 y + 2 z = - 3 - 14$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 3.1.2

Subtract $2 z$ from both sides of the equation.

$- 5 y = - 3 - 14 - 2 z$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 3.1.3

Subtract $14$ from $- 3$ .

$- 5 y = - 17 - 2 z$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$- 5 y = - 17 - 2 z$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 3.2

Divide each term in $- 5 y = - 17 - 2 z$ by $- 5$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 5 y = - 17 - 2 z$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 17}{- 5} + \frac{- 2 z}{- 5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 5$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 17}{- 5} + \frac{- 2 z}{- 5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 17}{- 5} + \frac{- 2 z}{- 5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$y = \frac{- 17}{- 5} + \frac{- 2 z}{- 5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$y = \frac{- 17}{- 5} + \frac{- 2 z}{- 5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

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.

$y = \frac{17}{5} + \frac{- 2 z}{- 5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 3.2.3.1.2

Dividing two negative values results in a positive value.

$y = \frac{17}{5} + \frac{2 z}{5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$y = \frac{17}{5} + \frac{2 z}{5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$y = \frac{17}{5} + \frac{2 z}{5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$y = \frac{17}{5} + \frac{2 z}{5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

$y = \frac{17}{5} + \frac{2 z}{5}$

$7 - 4 y - 5 z = 0$

$x = 7 - 2 y - z$

Step 4

Replace all occurrences of $y$ with $\frac{17}{5} + \frac{2 z}{5}$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $7 - 4 y - 5 z = 0$ with $\frac{17}{5} + \frac{2 z}{5}$ .

$7 - 4 (\frac{17}{5} + \frac{2 z}{5}) - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Simplify $7 - 4 (\frac{17}{5} + \frac{2 z}{5}) - 5 z$ .

Tap for more steps...

Step 4.2.1.1

Simplify each term.

Tap for more steps...

Step 4.2.1.1.1

Apply the distributive property.

$7 - 4 (\frac{17}{5}) - 4 \frac{2 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.1.2

Multiply $- 4 (\frac{17}{5})$ .

Tap for more steps...

Step 4.2.1.1.2.1

Combine $- 4$ and $\frac{17}{5}$ .

$7 + \frac{- 4 \cdot 17}{5} - 4 \frac{2 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.1.2.2

Multiply $- 4$ by $17$ .

$7 + \frac{- 68}{5} - 4 \frac{2 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

$7 + \frac{- 68}{5} - 4 \frac{2 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.1.3

Multiply $- 4 \frac{2 z}{5}$ .

Tap for more steps...

Step 4.2.1.1.3.1

Combine $- 4$ and $\frac{2 z}{5}$ .

$7 + \frac{- 68}{5} + \frac{- 4 (2 z)}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.1.3.2

Multiply $2$ by $- 4$ .

$7 + \frac{- 68}{5} + \frac{- 8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

$7 + \frac{- 68}{5} + \frac{- 8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.1.4

Simplify each term.

Tap for more steps...

Step 4.2.1.1.4.1

Move the negative in front of the fraction.

$7 - \frac{68}{5} + \frac{- 8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.1.4.2

Move the negative in front of the fraction.

$7 - \frac{68}{5} - \frac{8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

$7 - \frac{68}{5} - \frac{8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

$7 - \frac{68}{5} - \frac{8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$7 \cdot \frac{5}{5} - \frac{68}{5} - \frac{8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.3

Combine $7$ and $\frac{5}{5}$ .

$\frac{7 \cdot 5}{5} - \frac{68}{5} - \frac{8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.4

Combine the numerators over the common denominator.

$\frac{7 \cdot 5 - 68}{5} - \frac{8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.5

Simplify the numerator.

Tap for more steps...

Step 4.2.1.5.1

Multiply $7$ by $5$ .

$\frac{35 - 68}{5} - \frac{8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.5.2

Subtract $68$ from $35$ .

$\frac{- 33}{5} - \frac{8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

$\frac{- 33}{5} - \frac{8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.6

Move the negative in front of the fraction.

$- \frac{33}{5} - \frac{8 z}{5} - 5 z = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.7

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

$- \frac{33}{5} - \frac{8 z}{5} - 5 z \cdot \frac{5}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.8

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

$- \frac{33}{5} - \frac{8 z}{5} + \frac{- 5 z \cdot 5}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.9

Combine the numerators over the common denominator.

$- \frac{33}{5} + \frac{- 8 z - 5 z \cdot 5}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.10

Combine the numerators over the common denominator.

$\frac{- 33 - 8 z - 5 z \cdot 5}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.11

Multiply $5$ by $- 5$ .

$\frac{- 33 - 8 z - 25 z}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.12

Subtract $25 z$ from $- 8 z$ .

$\frac{- 33 - 33 z}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.13

Factor $33$ out of $- 33 - 33 z$ .

Tap for more steps...

Step 4.2.1.13.1

Factor $33$ out of $- 33$ .

$\frac{33 (- 1) - 33 z}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.13.2

Factor $33$ out of $- 33 z$ .

$\frac{33 (- 1) + 33 (- z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.13.3

Factor $33$ out of $33 (- 1) + 33 (- z)$ .

$\frac{33 (- 1 - z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

$\frac{33 (- 1 - z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.14

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

$\frac{33 (- 1 \cdot 1 - z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.15

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

$\frac{33 (- 1 \cdot 1 - (z))}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.16

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

$\frac{33 (- 1 (1 + z))}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.2.1.17

Move the negative in front of the fraction.

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - 2 y - z$

Step 4.3

Replace all occurrences of $y$ in $x = 7 - 2 y - z$ with $\frac{17}{5} + \frac{2 z}{5}$ .

$x = 7 - 2 (\frac{17}{5} + \frac{2 z}{5}) - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4

Simplify the right side.

Tap for more steps...

Step 4.4.1

Simplify $7 - 2 (\frac{17}{5} + \frac{2 z}{5}) - z$ .

Tap for more steps...

Step 4.4.1.1

Simplify each term.

Tap for more steps...

Step 4.4.1.1.1

Apply the distributive property.

$x = 7 - 2 (\frac{17}{5}) - 2 \frac{2 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.1.2

Multiply $- 2 (\frac{17}{5})$ .

Tap for more steps...

Step 4.4.1.1.2.1

Combine $- 2$ and $\frac{17}{5}$ .

$x = 7 + \frac{- 2 \cdot 17}{5} - 2 \frac{2 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.1.2.2

Multiply $- 2$ by $17$ .

$x = 7 + \frac{- 34}{5} - 2 \frac{2 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 + \frac{- 34}{5} - 2 \frac{2 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.1.3

Multiply $- 2 \frac{2 z}{5}$ .

Tap for more steps...

Step 4.4.1.1.3.1

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

$x = 7 + \frac{- 34}{5} + \frac{- 2 (2 z)}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.1.3.2

Multiply $2$ by $- 2$ .

$x = 7 + \frac{- 34}{5} + \frac{- 4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 + \frac{- 34}{5} + \frac{- 4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.1.4

Simplify each term.

Tap for more steps...

Step 4.4.1.1.4.1

Move the negative in front of the fraction.

$x = 7 - \frac{34}{5} + \frac{- 4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.1.4.2

Move the negative in front of the fraction.

$x = 7 - \frac{34}{5} - \frac{4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - \frac{34}{5} - \frac{4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 7 - \frac{34}{5} - \frac{4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = 7 \cdot \frac{5}{5} - \frac{34}{5} - \frac{4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.3

Combine $7$ and $\frac{5}{5}$ .

$x = \frac{7 \cdot 5}{5} - \frac{34}{5} - \frac{4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$x = \frac{7 \cdot 5 - 34}{5} - \frac{4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.5

Simplify the numerator.

Tap for more steps...

Step 4.4.1.5.1

Multiply $7$ by $5$ .

$x = \frac{35 - 34}{5} - \frac{4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.5.2

Subtract $34$ from $35$ .

$x = \frac{1}{5} - \frac{4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = \frac{1}{5} - \frac{4 z}{5} - z$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.6

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

$x = \frac{1}{5} - \frac{4 z}{5} - z \cdot \frac{5}{5}$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.7

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

$x = \frac{1}{5} - \frac{4 z}{5} + \frac{- z \cdot 5}{5}$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.8

Combine the numerators over the common denominator.

$x = \frac{1}{5} + \frac{- 4 z - z \cdot 5}{5}$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.9

Combine the numerators over the common denominator.

$x = \frac{1 - 4 z - z \cdot 5}{5}$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.10

Multiply $5$ by $- 1$ .

$x = \frac{1 - 4 z - 5 z}{5}$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 4.4.1.11

Subtract $5 z$ from $- 4 z$ .

$x = \frac{1 - 9 z}{5}$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = \frac{1 - 9 z}{5}$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = \frac{1 - 9 z}{5}$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = \frac{1 - 9 z}{5}$

$- \frac{33 (1 + z)}{5} = 0$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 5

Solve for $z$ in $- \frac{33 (1 + z)}{5} = 0$ .

Tap for more steps...

Step 5.1

Set the numerator equal to zero.

$33 (1 + z) = 0$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 5.2

Solve the equation for $z$ .

Tap for more steps...

Step 5.2.1

Divide each term in $33 (1 + z) = 0$ by $33$ and simplify.

Tap for more steps...

Step 5.2.1.1

Divide each term in $33 (1 + z) = 0$ by $33$ .

$\frac{33 (1 + z)}{33} = \frac{0}{33}$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 5.2.1.2

Simplify the left side.

Tap for more steps...

Step 5.2.1.2.1

Cancel the common factor of $33$ .

Tap for more steps...

Step 5.2.1.2.1.1

Cancel the common factor.

$\frac{33 (1 + z)}{33} = \frac{0}{33}$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 5.2.1.2.1.2

Divide $1 + z$ by $1$ .

$1 + z = \frac{0}{33}$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

$1 + z = \frac{0}{33}$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

$1 + z = \frac{0}{33}$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 5.2.1.3

Simplify the right side.

Tap for more steps...

Step 5.2.1.3.1

Divide $0$ by $33$ .

$1 + z = 0$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

$1 + z = 0$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

$1 + z = 0$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 5.2.2

Subtract $1$ from both sides of the equation.

$z = - 1$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

$z = - 1$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

$z = - 1$

$x = \frac{1 - 9 z}{5}$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 6

Replace all occurrences of $z$ with $- 1$ in each equation.

Tap for more steps...

Step 6.1

Replace all occurrences of $z$ in $x = \frac{1 - 9 z}{5}$ with $- 1$ .

$x = \frac{1 - 9 \cdot - 1}{5}$

$z = - 1$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify $\frac{1 - 9 \cdot - 1}{5}$ .

Tap for more steps...

Step 6.2.1.1

Simplify the numerator.

Tap for more steps...

Step 6.2.1.1.1

Multiply $- 9$ by $- 1$ .

$x = \frac{1 + 9}{5}$

$z = - 1$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 6.2.1.1.2

Add $1$ and $9$ .

$x = \frac{10}{5}$

$z = - 1$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = \frac{10}{5}$

$z = - 1$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 6.2.1.2

Divide $10$ by $5$ .

$x = 2$

$z = - 1$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 2$

$z = - 1$

$y = \frac{17}{5} + \frac{2 z}{5}$

$x = 2$

$z = - 1$

$y = \frac{17}{5} + \frac{2 z}{5}$

Step 6.3

Replace all occurrences of $z$ in $y = \frac{17}{5} + \frac{2 z}{5}$ with $- 1$ .

$y = \frac{17}{5} + \frac{2 (- 1)}{5}$

$x = 2$

$z = - 1$

Step 6.4

Simplify the right side.

Tap for more steps...

Step 6.4.1

Simplify $\frac{17}{5} + \frac{2 (- 1)}{5}$ .

Tap for more steps...

Step 6.4.1.1

Combine the numerators over the common denominator.

$y = \frac{17 + 2 (- 1)}{5}$

$x = 2$

$z = - 1$

Step 6.4.1.2

Simplify the expression.

Tap for more steps...

Step 6.4.1.2.1

Multiply $2$ by $- 1$ .

$y = \frac{17 - 2}{5}$

$x = 2$

$z = - 1$

Step 6.4.1.2.2

Subtract $2$ from $17$ .

$y = \frac{15}{5}$

$x = 2$

$z = - 1$

Step 6.4.1.2.3

Divide $15$ by $5$ .

$y = 3$

$x = 2$

$z = - 1$

$y = 3$

$x = 2$

$z = - 1$

$y = 3$

$x = 2$

$z = - 1$

$y = 3$

$x = 2$

$z = - 1$

$y = 3$

$x = 2$

$z = - 1$

Step 7

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

$(2, 3, - 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(2, 3, - 1)$

Equation Form:

$x = 2, y = 3, z = - 1$