Solve the System of Equations 4x-y+z=10 2x+y+3z=4 -3x+2y+2z=-7

$4 x - y + z = 10$ $2 x + y + 3 z = 4$ $- 3 x + 2 y + 2 z = - 7$

Step 1

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

Subtract $4 x$ from both sides of the equation.

$- y + z = 10 - 4 x$

$2 x + y + 3 z = 4$

$- 3 x + 2 y + 2 z = - 7$

Add $y$ to both sides of the equation.

$z = 10 - 4 x + y$

$2 x + y + 3 z = 4$

$- 3 x + 2 y + 2 z = - 7$

$z = 10 - 4 x + y$

$2 x + y + 3 z = 4$

$- 3 x + 2 y + 2 z = - 7$

Step 2

Replace all occurrences of $z$ with $10 - 4 x + y$ in each equation.

Replace all occurrences of $z$ in $2 x + y + 3 z = 4$ with $10 - 4 x + y$ .

$2 x + y + 3 (10 - 4 x + y) = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

Simplify the left side.

Simplify $2 x + y + 3 (10 - 4 x + y)$ .

Simplify each term.

Apply the distributive property.

$2 x + y + 3 \cdot 10 + 3 (- 4 x) + 3 y = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

Simplify.

Multiply $3$ by $10$ .

$2 x + y + 30 + 3 (- 4 x) + 3 y = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

Multiply $- 4$ by $3$ .

$2 x + y + 30 - 12 x + 3 y = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

$2 x + y + 30 - 12 x + 3 y = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

$2 x + y + 30 - 12 x + 3 y = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

Simplify by adding terms.

Subtract $12 x$ from $2 x$ .

$- 10 x + y + 30 + 3 y = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

Add $y$ and $3 y$ .

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 2 z = - 7$

Replace all occurrences of $z$ in $- 3 x + 2 y + 2 z = - 7$ with $10 - 4 x + y$ .

$- 3 x + 2 y + 2 (10 - 4 x + y) = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Simplify the left side.

Simplify $- 3 x + 2 y + 2 (10 - 4 x + y)$ .

Simplify each term.

Apply the distributive property.

$- 3 x + 2 y + 2 \cdot 10 + 2 (- 4 x) + 2 y = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Simplify.

Multiply $2$ by $10$ .

$- 3 x + 2 y + 20 + 2 (- 4 x) + 2 y = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Multiply $- 4$ by $2$ .

$- 3 x + 2 y + 20 - 8 x + 2 y = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 20 - 8 x + 2 y = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 3 x + 2 y + 20 - 8 x + 2 y = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Simplify by adding terms.

Subtract $8 x$ from $- 3 x$ .

$- 11 x + 2 y + 20 + 2 y = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Add $2 y$ and $2 y$ .

$- 11 x + 4 y + 20 = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 11 x + 4 y + 20 = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 11 x + 4 y + 20 = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 11 x + 4 y + 20 = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 11 x + 4 y + 20 = - 7$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Step 3

Solve for $x$ in $- 11 x + 4 y + 20 = - 7$ .

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

Subtract $4 y$ from both sides of the equation.

$- 11 x + 20 = - 7 - 4 y$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Subtract $20$ from both sides of the equation.

$- 11 x = - 7 - 4 y - 20$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Subtract $20$ from $- 7$ .

$- 11 x = - 4 y - 27$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$- 11 x = - 4 y - 27$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Divide each term in $- 11 x = - 4 y - 27$ by $- 11$ and simplify.

Divide each term in $- 11 x = - 4 y - 27$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{- 4 y}{- 11} + \frac{- 27}{- 11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{- 4 y}{- 11} + \frac{- 27}{- 11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Divide $x$ by $1$ .

$x = \frac{- 4 y}{- 11} + \frac{- 27}{- 11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$x = \frac{- 4 y}{- 11} + \frac{- 27}{- 11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$x = \frac{- 4 y}{- 11} + \frac{- 27}{- 11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{(4) y}{11} + \frac{- 27}{- 11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Dividing two negative values results in a positive value.

$x = \frac{4 y}{11} + \frac{27}{11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$x = \frac{4 y}{11} + \frac{27}{11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$x = \frac{4 y}{11} + \frac{27}{11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$x = \frac{4 y}{11} + \frac{27}{11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

$x = \frac{4 y}{11} + \frac{27}{11}$

$- 10 x + 4 y + 30 = 4$

$z = 10 - 4 x + y$

Step 4

Replace all occurrences of $x$ with $\frac{4 y}{11} + \frac{27}{11}$ in each equation.

Replace all occurrences of $x$ in $- 10 x + 4 y + 30 = 4$ with $\frac{4 y}{11} + \frac{27}{11}$ .

$- 10 (\frac{4 y}{11} + \frac{27}{11}) + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Simplify the left side.

Simplify $- 10 (\frac{4 y}{11} + \frac{27}{11}) + 4 y + 30$ .

Simplify each term.

Apply the distributive property.

$- 10 \frac{4 y}{11} - 10 (\frac{27}{11}) + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Multiply $- 10 \frac{4 y}{11}$ .

Combine $- 10$ and $\frac{4 y}{11}$ .

$\frac{- 10 (4 y)}{11} - 10 (\frac{27}{11}) + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Multiply $4$ by $- 10$ .

$\frac{- 40 y}{11} - 10 (\frac{27}{11}) + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$\frac{- 40 y}{11} - 10 (\frac{27}{11}) + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Multiply $- 10 (\frac{27}{11})$ .

Combine $- 10$ and $\frac{27}{11}$ .

$\frac{- 40 y}{11} + \frac{- 10 \cdot 27}{11} + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Multiply $- 10$ by $27$ .

$\frac{- 40 y}{11} + \frac{- 270}{11} + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$\frac{- 40 y}{11} + \frac{- 270}{11} + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{(40) y}{11} + \frac{- 270}{11} + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Move the negative in front of the fraction.

$- \frac{40 y}{11} - \frac{270}{11} + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$- \frac{40 y}{11} - \frac{270}{11} + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$- \frac{40 y}{11} - \frac{270}{11} + 4 y + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

To write $4 y$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$- \frac{40 y}{11} + 4 y \cdot \frac{11}{11} - \frac{270}{11} + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Combine $4 y$ and $\frac{11}{11}$ .

$- \frac{40 y}{11} + \frac{4 y \cdot 11}{11} - \frac{270}{11} + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Combine the numerators over the common denominator.

$\frac{- 40 y + 4 y \cdot 11}{11} - \frac{270}{11} + 30 = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Combine the numerators over the common denominator.

$30 + \frac{- 40 y + 4 y \cdot 11 - 270}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Multiply $11$ by $4$ .

$30 + \frac{- 40 y + 44 y - 270}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Add $- 40 y$ and $44 y$ .

$30 + \frac{4 y - 270}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Factor $2$ out of $4 y - 270$ .

Factor $2$ out of $4 y$ .

$30 + \frac{2 (2 y) - 270}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Factor $2$ out of $- 270$ .

$30 + \frac{2 (2 y) + 2 (- 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Factor $2$ out of $2 (2 y) + 2 (- 135)$ .

$30 + \frac{2 (2 y - 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$30 + \frac{2 (2 y - 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

To write $30$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$30 \cdot \frac{11}{11} + \frac{2 (2 y - 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Simplify terms.

Combine $30$ and $\frac{11}{11}$ .

$\frac{30 \cdot 11}{11} + \frac{2 (2 y - 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Combine the numerators over the common denominator.

$\frac{30 \cdot 11 + 2 (2 y - 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$\frac{30 \cdot 11 + 2 (2 y - 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Simplify the numerator.

Factor $2$ out of $30 \cdot 11 + 2 (2 y - 135)$ .

Factor $2$ out of $30 \cdot 11$ .

$\frac{2 (15 \cdot 11) + 2 (2 y - 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Factor $2$ out of $2 (15 \cdot 11) + 2 (2 y - 135)$ .

$\frac{2 (15 \cdot 11 + 2 y - 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$\frac{2 (15 \cdot 11 + 2 y - 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Multiply $15$ by $11$ .

$\frac{2 (165 + 2 y - 135)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Subtract $135$ from $165$ .

$\frac{2 (2 y + 30)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Factor $2$ out of $2 y + 30$ .

Factor $2$ out of $2 y$ .

$\frac{2 (2 (y) + 30)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Factor $2$ out of $30$ .

$\frac{2 (2 y + 2 \cdot 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Factor $2$ out of $2 y + 2 \cdot 15$ .

$\frac{2 (2 (y + 15))}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$\frac{2 \cdot (2 (y + 15))}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Multiply $2$ by $2$ .

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - 4 x + y$

Replace all occurrences of $x$ in $z = 10 - 4 x + y$ with $\frac{4 y}{11} + \frac{27}{11}$ .

$z = 10 - 4 (\frac{4 y}{11} + \frac{27}{11}) + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Simplify the right side.

Simplify $10 - 4 (\frac{4 y}{11} + \frac{27}{11}) + y$ .

Simplify each term.

Apply the distributive property.

$z = 10 - 4 \frac{4 y}{11} - 4 (\frac{27}{11}) + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Multiply $- 4 \frac{4 y}{11}$ .

Combine $- 4$ and $\frac{4 y}{11}$ .

$z = 10 + \frac{- 4 (4 y)}{11} - 4 (\frac{27}{11}) + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Multiply $4$ by $- 4$ .

$z = 10 + \frac{- 16 y}{11} - 4 (\frac{27}{11}) + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 + \frac{- 16 y}{11} - 4 (\frac{27}{11}) + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Multiply $- 4 (\frac{27}{11})$ .

Combine $- 4$ and $\frac{27}{11}$ .

$z = 10 + \frac{- 16 y}{11} + \frac{- 4 \cdot 27}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Multiply $- 4$ by $27$ .

$z = 10 + \frac{- 16 y}{11} + \frac{- 108}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 + \frac{- 16 y}{11} + \frac{- 108}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Simplify each term.

Move the negative in front of the fraction.

$z = 10 - \frac{(16) y}{11} + \frac{- 108}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Move the negative in front of the fraction.

$z = 10 - \frac{16 y}{11} - \frac{108}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - \frac{16 y}{11} - \frac{108}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 10 - \frac{16 y}{11} - \frac{108}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

To write $10$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$z = - \frac{16 y}{11} + 10 \cdot \frac{11}{11} - \frac{108}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Combine $10$ and $\frac{11}{11}$ .

$z = - \frac{16 y}{11} + \frac{10 \cdot 11}{11} - \frac{108}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Combine the numerators over the common denominator.

$z = - \frac{16 y}{11} + \frac{10 \cdot 11 - 108}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Simplify the numerator.

Multiply $10$ by $11$ .

$z = - \frac{16 y}{11} + \frac{110 - 108}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Subtract $108$ from $110$ .

$z = - \frac{16 y}{11} + \frac{2}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = - \frac{16 y}{11} + \frac{2}{11} + y$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

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

$z = - \frac{16 y}{11} + y \cdot \frac{11}{11} + \frac{2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Simplify terms.

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

$z = - \frac{16 y}{11} + \frac{y \cdot 11}{11} + \frac{2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Combine the numerators over the common denominator.

$z = \frac{- 16 y + y \cdot 11}{11} + \frac{2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Combine the numerators over the common denominator.

$z = \frac{- 16 y + y \cdot 11 + 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = \frac{- 16 y + y \cdot 11 + 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Move $11$ to the left of $y$ .

$z = \frac{- 16 y + 11 y + 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Simplify terms.

Add $- 16 y$ and $11 y$ .

$z = \frac{- 5 y + 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Factor $- 1$ out of $- 5 y$ .

$z = \frac{- (5 y) + 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Rewrite $2$ as $- 1 (- 2)$ .

$z = \frac{- (5 y) - 1 \cdot - 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Factor $- 1$ out of $- (5 y) - 1 (- 2)$ .

$z = \frac{- (5 y - 2)}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Simplify the expression.

Rewrite $- (5 y - 2)$ as $- 1 (5 y - 2)$ .

$z = \frac{- 1 (5 y - 2)}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Move the negative in front of the fraction.

$z = - \frac{5 y - 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = - \frac{5 y - 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = - \frac{5 y - 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = - \frac{5 y - 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = - \frac{5 y - 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = - \frac{5 y - 2}{11}$

$\frac{4 (y + 15)}{11} = 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Step 5

Solve for $y$ in $\frac{4 (y + 15)}{11} = 4$ .

Multiply both sides of the equation by $\frac{11}{4}$ .

$\frac{11}{4} \cdot \frac{4 (y + 15)}{11} = \frac{11}{4} \cdot 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{11}{4} \cdot \frac{4 (y + 15)}{11}$ .

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11}{4} \cdot \frac{4 (y + 15)}{11} = \frac{11}{4} \cdot 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

Rewrite the expression.

$\frac{1}{4} \cdot (4 (y + 15)) = \frac{11}{4} \cdot 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

$\frac{1}{4} \cdot (4 (y + 15)) = \frac{11}{4} \cdot 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{1}{4} \cdot (4 (y + 15)) = \frac{11}{4} \cdot 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

Rewrite the expression.

$y + 15 = \frac{11}{4} \cdot 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

$y + 15 = \frac{11}{4} \cdot 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

$y + 15 = \frac{11}{4} \cdot 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

$y + 15 = \frac{11}{4} \cdot 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

Simplify the right side.

Cancel the common factor of $4$ .

Cancel the common factor.

$y + 15 = \frac{11}{4} \cdot 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

Rewrite the expression.

$y + 15 = 11$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

$y + 15 = 11$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

$y + 15 = 11$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

$y + 15 = 11$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

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

Subtract $15$ from both sides of the equation.

$y = 11 - 15$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

Subtract $15$ from $11$ .

$y = - 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

$y = - 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

$y = - 4$

$z = - \frac{5 y - 2}{11}$

$x = \frac{4 y}{11} + \frac{27}{11}$

Step 6

Replace all occurrences of $y$ with $- 4$ in each equation.

Replace all occurrences of $y$ in $z = - \frac{5 y - 2}{11}$ with $- 4$ .

$z = - \frac{5 (- 4) - 2}{11}$

$y = - 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Simplify the right side.

Simplify $- \frac{5 (- 4) - 2}{11}$ .

Simplify the numerator.

Multiply $5$ by $- 4$ .

$z = - \frac{- 20 - 2}{11}$

$y = - 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Subtract $2$ from $- 20$ .

$z = - \frac{- 22}{11}$

$y = - 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = - \frac{- 22}{11}$

$y = - 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Simplify the expression.

Divide $- 22$ by $11$ .

$z = 2$

$y = - 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Multiply $- 1$ by $- 2$ .

$z = 2$

$y = - 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 2$

$y = - 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 2$

$y = - 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

$z = 2$

$y = - 4$

$x = \frac{4 y}{11} + \frac{27}{11}$

Replace all occurrences of $y$ in $x = \frac{4 y}{11} + \frac{27}{11}$ with $- 4$ .

$x = \frac{4 (- 4)}{11} + \frac{27}{11}$

$z = 2$

$y = - 4$

Simplify the right side.

Simplify $\frac{4 (- 4)}{11} + \frac{27}{11}$ .

Combine the numerators over the common denominator.

$x = \frac{4 (- 4) + 27}{11}$

$z = 2$

$y = - 4$

Simplify the expression.

Multiply $4$ by $- 4$ .

$x = \frac{- 16 + 27}{11}$

$z = 2$

$y = - 4$

Add $- 16$ and $27$ .

$x = \frac{11}{11}$

$z = 2$

$y = - 4$

Divide $11$ by $11$ .

$x = 1$

$z = 2$

$y = - 4$

$x = 1$

$z = 2$

$y = - 4$

$x = 1$

$z = 2$

$y = - 4$

$x = 1$

$z = 2$

$y = - 4$

$x = 1$

$z = 2$

$y = - 4$

Step 7

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

$(1, - 4, 2)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(1, - 4, 2)$

Equation Form:

$x = 1, y = - 4, z = 2$

Solve the System of Equations 4x-y+z=10 2x+y+3z=4 -3x+2y+2z=-7

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