Solve the System of Equations x+y+z=-5 -x+6y-4z=-8 -x+4y+2z=6

$x + y + z = - 5$ $- x + 6 y - 4 z = - 8$ $- x + 4 y + 2 z = 6$

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

Subtract $y$ from both sides of the equation.

$x + z = - 5 - y$

$- x + 6 y - 4 z = - 8$

$- x + 4 y + 2 z = 6$

Subtract $z$ from both sides of the equation.

$x = - 5 - y - z$

$- x + 6 y - 4 z = - 8$

$- x + 4 y + 2 z = 6$

$x = - 5 - y - z$

$- x + 6 y - 4 z = - 8$

$- x + 4 y + 2 z = 6$

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

Replace all occurrences of $x$ in $- x + 6 y - 4 z = - 8$ with $- 5 - y - z$ .

$- (- 5 - y - z) + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

Simplify the left side.

Simplify $- (- 5 - y - z) + 6 y - 4 z$ .

Simplify each term.

Apply the distributive property.

$5 + y + z + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

Simplify.

Multiply $- 1$ by $- 5$ .

$5 + y + z + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

Multiply $- - y$ .

Multiply $- 1$ by $- 1$ .

$5 + 1 y + z + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

Multiply $y$ by $1$ .

$5 + y + z + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

$5 + y + z + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

Multiply $- - z$ .

Multiply $- 1$ by $- 1$ .

$5 + y + 1 z + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

Multiply $z$ by $1$ .

$5 + y + z + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

$5 + y + z + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

$5 + y + z + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

$5 + y + z + 6 y - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

Simplify by adding terms.

Add $y$ and $6 y$ .

$5 + 7 y + z - 4 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

Subtract $4 z$ from $z$ .

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$- x + 4 y + 2 z = 6$

Replace all occurrences of $x$ in $- x + 4 y + 2 z = 6$ with $- 5 - y - z$ .

$- (- 5 - y - z) + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Simplify the left side.

Simplify $- (- 5 - y - z) + 4 y + 2 z$ .

Simplify each term.

Apply the distributive property.

$5 + y + z + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Simplify.

Multiply $- 1$ by $- 5$ .

$5 + y + z + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Multiply $- - y$ .

Multiply $- 1$ by $- 1$ .

$5 + 1 y + z + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Multiply $y$ by $1$ .

$5 + y + z + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$5 + y + z + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Multiply $- - z$ .

Multiply $- 1$ by $- 1$ .

$5 + y + 1 z + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Multiply $z$ by $1$ .

$5 + y + z + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$5 + y + z + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$5 + y + z + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$5 + y + z + 4 y + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Simplify by adding terms.

Add $y$ and $4 y$ .

$5 + 5 y + z + 2 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Add $z$ and $2 z$ .

$5 + 5 y + 3 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$5 + 5 y + 3 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$5 + 5 y + 3 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$5 + 5 y + 3 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$5 + 5 y + 3 z = 6$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Solve for $y$ in $5 + 5 y + 3 z = 6$ .

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

Subtract $5$ from both sides of the equation.

$5 y + 3 z = 6 - 5$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Subtract $3 z$ from both sides of the equation.

$5 y = 6 - 5 - 3 z$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Subtract $5$ from $6$ .

$5 y = 1 - 3 z$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$5 y = 1 - 3 z$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Divide each term in $5 y = 1 - 3 z$ by $5$ and simplify.

Divide each term in $5 y = 1 - 3 z$ by $5$ .

$\frac{5 y}{5} = \frac{1}{5} + \frac{- 3 z}{5}$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{1}{5} + \frac{- 3 z}{5}$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Divide $y$ by $1$ .

$y = \frac{1}{5} + \frac{- 3 z}{5}$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$y = \frac{1}{5} + \frac{- 3 z}{5}$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$y = \frac{1}{5} + \frac{- 3 z}{5}$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{1}{5} - \frac{3 z}{5}$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$y = \frac{1}{5} - \frac{3 z}{5}$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$y = \frac{1}{5} - \frac{3 z}{5}$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

$y = \frac{1}{5} - \frac{3 z}{5}$

$5 + 7 y - 3 z = - 8$

$x = - 5 - y - z$

Replace all occurrences of $y$ with $\frac{1}{5} - \frac{3 z}{5}$ in each equation.

Replace all occurrences of $y$ in $5 + 7 y - 3 z = - 8$ with $\frac{1}{5} - \frac{3 z}{5}$ .

$5 + 7 (\frac{1}{5} - \frac{3 z}{5}) - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Simplify the left side.

Simplify $5 + 7 (\frac{1}{5} - \frac{3 z}{5}) - 3 z$ .

Simplify each term.

Apply the distributive property.

$5 + 7 (\frac{1}{5}) + 7 (- \frac{3 z}{5}) - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Combine $7$ and $\frac{1}{5}$ .

$5 + \frac{7}{5} + 7 (- \frac{3 z}{5}) - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Multiply $7 (- \frac{3 z}{5})$ .

Multiply $- 1$ by $7$ .

$5 + \frac{7}{5} - 7 \frac{3 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Combine $- 7$ and $\frac{3 z}{5}$ .

$5 + \frac{7}{5} + \frac{- 7 (3 z)}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Multiply $3$ by $- 7$ .

$5 + \frac{7}{5} + \frac{- 21 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

$5 + \frac{7}{5} + \frac{- 21 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Move the negative in front of the fraction.

$5 + \frac{7}{5} - \frac{21 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

$5 + \frac{7}{5} - \frac{21 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

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

$5 \cdot \frac{5}{5} + \frac{7}{5} - \frac{21 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

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

$\frac{5 \cdot 5}{5} + \frac{7}{5} - \frac{21 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 + 7}{5} - \frac{21 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Simplify the numerator.

Multiply $5$ by $5$ .

$\frac{25 + 7}{5} - \frac{21 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Add $25$ and $7$ .

$\frac{32}{5} - \frac{21 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

$\frac{32}{5} - \frac{21 z}{5} - 3 z = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

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

$\frac{32}{5} - \frac{21 z}{5} - 3 z \cdot \frac{5}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Combine $- 3 z$ and $\frac{5}{5}$ .

$\frac{32}{5} - \frac{21 z}{5} + \frac{- 3 z \cdot 5}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Combine the numerators over the common denominator.

$\frac{32}{5} + \frac{- 21 z - 3 z \cdot 5}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Combine the numerators over the common denominator.

$\frac{32 - 21 z - 3 z \cdot 5}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Multiply $5$ by $- 3$ .

$\frac{32 - 21 z - 15 z}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Subtract $15 z$ from $- 21 z$ .

$\frac{32 - 36 z}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Factor $4$ out of $32 - 36 z$ .

Factor $4$ out of $32$ .

$\frac{4 (8) - 36 z}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Factor $4$ out of $- 36 z$ .

$\frac{4 (8) + 4 (- 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Factor $4$ out of $4 (8) + 4 (- 9 z)$ .

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - y - z$

Replace all occurrences of $y$ in $x = - 5 - y - z$ with $\frac{1}{5} - \frac{3 z}{5}$ .

$x = - 5 - (\frac{1}{5} - \frac{3 z}{5}) - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Simplify the right side.

Simplify $- 5 - (\frac{1}{5} - \frac{3 z}{5}) - z$ .

Simplify each term.

Apply the distributive property.

$x = - 5 - \frac{1}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Multiply $- - \frac{3 z}{5}$ .

Multiply $- 1$ by $- 1$ .

$x = - 5 - \frac{1}{5} + 1 (\frac{3 z}{5}) - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Multiply $\frac{3 z}{5}$ by $1$ .

$x = - 5 - \frac{1}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - \frac{1}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 5 - \frac{1}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

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

$x = - 5 \cdot \frac{5}{5} - \frac{1}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

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

$x = \frac{- 5 \cdot 5}{5} - \frac{1}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Combine the numerators over the common denominator.

$x = \frac{- 5 \cdot 5 - 1}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Simplify the numerator.

Multiply $- 5$ by $5$ .

$x = \frac{- 25 - 1}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Subtract $1$ from $- 25$ .

$x = \frac{- 26}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = \frac{- 26}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Move the negative in front of the fraction.

$x = - \frac{26}{5} + \frac{3 z}{5} - z$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

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

$x = - \frac{26}{5} + \frac{3 z}{5} - z \cdot \frac{5}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

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

$x = - \frac{26}{5} + \frac{3 z}{5} + \frac{- z \cdot 5}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Combine the numerators over the common denominator.

$x = - \frac{26}{5} + \frac{3 z - z \cdot 5}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Combine the numerators over the common denominator.

$x = \frac{- 26 + 3 z - z \cdot 5}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Multiply $5$ by $- 1$ .

$x = \frac{- 26 + 3 z - 5 z}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Subtract $5 z$ from $3 z$ .

$x = \frac{- 26 - 2 z}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Factor $2$ out of $- 26 - 2 z$ .

Factor $2$ out of $- 26$ .

$x = \frac{2 (- 13) - 2 z}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

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

$x = \frac{2 (- 13) + 2 (- z)}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Factor $2$ out of $2 (- 13) + 2 (- z)$ .

$x = \frac{2 (- 13 - z)}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = \frac{2 (- 13 - z)}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Rewrite $- 13$ as $- 1 (13)$ .

$x = \frac{2 (- 1 \cdot 13 - z)}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

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

$x = \frac{2 (- 1 \cdot 13 - (z))}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

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

$x = \frac{2 (- 1 (13 + z))}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Move the negative in front of the fraction.

$x = - \frac{2 (13 + z)}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - \frac{2 (13 + z)}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - \frac{2 (13 + z)}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - \frac{2 (13 + z)}{5}$

$\frac{4 (8 - 9 z)}{5} = - 8$

$y = \frac{1}{5} - \frac{3 z}{5}$

Solve for $z$ in $\frac{4 (8 - 9 z)}{5} = - 8$ .

Multiply both sides by $5$ .

$\frac{4 (8 - 9 z)}{5} \cdot 5 = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Simplify.

Simplify the left side.

Simplify $\frac{4 (8 - 9 z)}{5} \cdot 5$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{4 (8 - 9 z)}{5} \cdot 5 = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Rewrite the expression.

$4 (8 - 9 z) = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$4 (8 - 9 z) = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Apply the distributive property.

$4 \cdot 8 + 4 (- 9 z) = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Simplify the expression.

Multiply $4$ by $8$ .

$32 + 4 (- 9 z) = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Multiply $- 9$ by $4$ .

$32 - 36 z = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Reorder $32$ and $- 36 z$ .

$- 36 z + 32 = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$- 36 z + 32 = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$- 36 z + 32 = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$- 36 z + 32 = - 8 \cdot 5$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Simplify the right side.

Multiply $- 8$ by $5$ .

$- 36 z + 32 = - 40$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$- 36 z + 32 = - 40$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$- 36 z + 32 = - 40$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Solve for $z$ .

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

Subtract $32$ from both sides of the equation.

$- 36 z = - 40 - 32$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Subtract $32$ from $- 40$ .

$- 36 z = - 72$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$- 36 z = - 72$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Divide each term in $- 36 z = - 72$ by $- 36$ and simplify.

Divide each term in $- 36 z = - 72$ by $- 36$ .

$\frac{- 36 z}{- 36} = \frac{- 72}{- 36}$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Simplify the left side.

Cancel the common factor of $- 36$ .

Cancel the common factor.

$\frac{- 36 z}{- 36} = \frac{- 72}{- 36}$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Divide $z$ by $1$ .

$z = \frac{- 72}{- 36}$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$z = \frac{- 72}{- 36}$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$z = \frac{- 72}{- 36}$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Simplify the right side.

Divide $- 72$ by $- 36$ .

$z = 2$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$z = 2$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$z = 2$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$z = 2$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

$z = 2$

$x = - \frac{2 (13 + z)}{5}$

$y = \frac{1}{5} - \frac{3 z}{5}$

Replace all occurrences of $z$ with $2$ in each equation.

Replace all occurrences of $z$ in $x = - \frac{2 (13 + z)}{5}$ with $2$ .

$x = - \frac{2 (13 + 2)}{5}$

$z = 2$

$y = \frac{1}{5} - \frac{3 z}{5}$

Simplify $x = - \frac{2 (13 + 2)}{5}$ .

Simplify the left side.

Remove parentheses.

$x = - \frac{2 (13 + 2)}{5}$

$z = 2$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - \frac{2 (13 + 2)}{5}$

$z = 2$

$y = \frac{1}{5} - \frac{3 z}{5}$

Simplify the right side.

Simplify $- \frac{2 (13 + 2)}{5}$ .

Add $13$ and $2$ .

$x = - \frac{2 \cdot 15}{5}$

$z = 2$

$y = \frac{1}{5} - \frac{3 z}{5}$

Multiply $2$ by $15$ .

$x = - \frac{30}{5}$

$z = 2$

$y = \frac{1}{5} - \frac{3 z}{5}$

Divide $30$ by $5$ .

$x = - 1 \cdot 6$

$z = 2$

$y = \frac{1}{5} - \frac{3 z}{5}$

Multiply $- 1$ by $6$ .

$x = - 6$

$z = 2$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 6$

$z = 2$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 6$

$z = 2$

$y = \frac{1}{5} - \frac{3 z}{5}$

$x = - 6$

$z = 2$

$y = \frac{1}{5} - \frac{3 z}{5}$

Replace all occurrences of $z$ in $y = \frac{1}{5} - \frac{3 z}{5}$ with $2$ .

$y = \frac{1}{5} - \frac{3 (2)}{5}$

$x = - 6$

$z = 2$

Simplify the right side.

Simplify $\frac{1}{5} - \frac{3 (2)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{1 - 3 \cdot 2}{5}$

$x = - 6$

$z = 2$

Simplify the expression.

Multiply $- 3$ by $2$ .

$y = \frac{1 - 6}{5}$

$x = - 6$

$z = 2$

Subtract $6$ from $1$ .

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

$x = - 6$

$z = 2$

Divide $- 5$ by $5$ .

$y = - 1$

$x = - 6$

$z = 2$

$y = - 1$

$x = - 6$

$z = 2$

$y = - 1$

$x = - 6$

$z = 2$

$y = - 1$

$x = - 6$

$z = 2$

$y = - 1$

$x = - 6$

$z = 2$

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

$(- 6, - 1, 2)$

The result can be shown in multiple forms.

Point Form:

$(- 6, - 1, 2)$

Equation Form:

$x = - 6, y = - 1, z = 2$

Solve the System of Equations x+y+z=-5 -x+6y-4z=-8 -x+4y+2z=6

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