Solve the System of Equations 2x+y-z=9 -x+6y+2z=-17 5x+7y+z=4

$2 x + y - z = 9$ $- x + 6 y + 2 z = - 17$ $5 x + 7 y + z = 4$

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

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

$y - z = 9 - 2 x$

$- x + 6 y + 2 z = - 17$

$5 x + 7 y + z = 4$

Add $z$ to both sides of the equation.

$y = 9 - 2 x + z$

$- x + 6 y + 2 z = - 17$

$5 x + 7 y + z = 4$

$y = 9 - 2 x + z$

$- x + 6 y + 2 z = - 17$

$5 x + 7 y + z = 4$

Replace all occurrences of $y$ with $9 - 2 x + z$ in each equation.

Replace all occurrences of $y$ in $- x + 6 y + 2 z = - 17$ with $9 - 2 x + z$ .

$- x + 6 (9 - 2 x + z) + 2 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

Simplify the left side.

Simplify $- x + 6 (9 - 2 x + z) + 2 z$ .

Simplify each term.

Apply the distributive property.

$- x + 6 \cdot 9 + 6 (- 2 x) + 6 z + 2 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

Simplify.

Multiply $6$ by $9$ .

$- x + 54 + 6 (- 2 x) + 6 z + 2 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

Multiply $- 2$ by $6$ .

$- x + 54 - 12 x + 6 z + 2 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

$- x + 54 - 12 x + 6 z + 2 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

$- x + 54 - 12 x + 6 z + 2 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

Simplify by adding terms.

Subtract $12 x$ from $- x$ .

$- 13 x + 54 + 6 z + 2 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

Add $6 z$ and $2 z$ .

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$5 x + 7 y + z = 4$

Replace all occurrences of $y$ in $5 x + 7 y + z = 4$ with $9 - 2 x + z$ .

$5 x + 7 (9 - 2 x + z) + z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Simplify the left side.

Simplify $5 x + 7 (9 - 2 x + z) + z$ .

Simplify each term.

Apply the distributive property.

$5 x + 7 \cdot 9 + 7 (- 2 x) + 7 z + z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Simplify.

Multiply $7$ by $9$ .

$5 x + 63 + 7 (- 2 x) + 7 z + z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Multiply $- 2$ by $7$ .

$5 x + 63 - 14 x + 7 z + z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$5 x + 63 - 14 x + 7 z + z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$5 x + 63 - 14 x + 7 z + z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Simplify by adding terms.

Subtract $14 x$ from $5 x$ .

$- 9 x + 63 + 7 z + z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Add $7 z$ and $z$ .

$- 9 x + 63 + 8 z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$- 9 x + 63 + 8 z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$- 9 x + 63 + 8 z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$- 9 x + 63 + 8 z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$- 9 x + 63 + 8 z = 4$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Solve for $x$ in $- 9 x + 63 + 8 z = 4$ .

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

Subtract $63$ from both sides of the equation.

$- 9 x + 8 z = 4 - 63$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Subtract $8 z$ from both sides of the equation.

$- 9 x = 4 - 63 - 8 z$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Subtract $63$ from $4$ .

$- 9 x = - 59 - 8 z$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$- 9 x = - 59 - 8 z$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Divide each term in $- 9 x = - 59 - 8 z$ by $- 9$ and simplify.

Divide each term in $- 9 x = - 59 - 8 z$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{- 59}{- 9} + \frac{- 8 z}{- 9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{- 59}{- 9} + \frac{- 8 z}{- 9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Divide $x$ by $1$ .

$x = \frac{- 59}{- 9} + \frac{- 8 z}{- 9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$x = \frac{- 59}{- 9} + \frac{- 8 z}{- 9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$x = \frac{- 59}{- 9} + \frac{- 8 z}{- 9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{59}{9} + \frac{- 8 z}{- 9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Dividing two negative values results in a positive value.

$x = \frac{59}{9} + \frac{8 z}{9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$x = \frac{59}{9} + \frac{8 z}{9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$x = \frac{59}{9} + \frac{8 z}{9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$x = \frac{59}{9} + \frac{8 z}{9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

$x = \frac{59}{9} + \frac{8 z}{9}$

$- 13 x + 54 + 8 z = - 17$

$y = 9 - 2 x + z$

Replace all occurrences of $x$ with $\frac{59}{9} + \frac{8 z}{9}$ in each equation.

Replace all occurrences of $x$ in $- 13 x + 54 + 8 z = - 17$ with $\frac{59}{9} + \frac{8 z}{9}$ .

$- 13 (\frac{59}{9} + \frac{8 z}{9}) + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Simplify the left side.

Simplify $- 13 (\frac{59}{9} + \frac{8 z}{9}) + 54 + 8 z$ .

Simplify each term.

Apply the distributive property.

$- 13 (\frac{59}{9}) - 13 \frac{8 z}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Multiply $- 13 (\frac{59}{9})$ .

Combine $- 13$ and $\frac{59}{9}$ .

$\frac{- 13 \cdot 59}{9} - 13 \frac{8 z}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Multiply $- 13$ by $59$ .

$\frac{- 767}{9} - 13 \frac{8 z}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

$\frac{- 767}{9} - 13 \frac{8 z}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Multiply $- 13 \frac{8 z}{9}$ .

Combine $- 13$ and $\frac{8 z}{9}$ .

$\frac{- 767}{9} + \frac{- 13 (8 z)}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Multiply $8$ by $- 13$ .

$\frac{- 767}{9} + \frac{- 104 z}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

$\frac{- 767}{9} + \frac{- 104 z}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{767}{9} + \frac{- 104 z}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Move the negative in front of the fraction.

$- \frac{767}{9} - \frac{104 z}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

$- \frac{767}{9} - \frac{104 z}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

$- \frac{767}{9} - \frac{104 z}{9} + 54 + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

To write $54$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{104 z}{9} - \frac{767}{9} + 54 \cdot \frac{9}{9} + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Combine $54$ and $\frac{9}{9}$ .

$- \frac{104 z}{9} - \frac{767}{9} + \frac{54 \cdot 9}{9} + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Combine the numerators over the common denominator.

$- \frac{104 z}{9} + \frac{- 767 + 54 \cdot 9}{9} + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Simplify the numerator.

Multiply $54$ by $9$ .

$- \frac{104 z}{9} + \frac{- 767 + 486}{9} + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Add $- 767$ and $486$ .

$- \frac{104 z}{9} + \frac{- 281}{9} + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

$- \frac{104 z}{9} + \frac{- 281}{9} + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Move the negative in front of the fraction.

$- \frac{104 z}{9} - \frac{281}{9} + 8 z = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

To write $8 z$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{104 z}{9} + 8 z \cdot \frac{9}{9} - \frac{281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Combine $8 z$ and $\frac{9}{9}$ .

$- \frac{104 z}{9} + \frac{8 z \cdot 9}{9} - \frac{281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Combine the numerators over the common denominator.

$\frac{- 104 z + 8 z \cdot 9}{9} - \frac{281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Combine the numerators over the common denominator.

$\frac{- 104 z + 8 z \cdot 9 - 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Multiply $9$ by $8$ .

$\frac{- 104 z + 72 z - 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Add $- 104 z$ and $72 z$ .

$\frac{- 32 z - 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Factor $- 1$ out of $- 32 z$ .

$\frac{- (32 z) - 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Rewrite $- 281$ as $- 1 (281)$ .

$\frac{- (32 z) - 1 \cdot 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Factor $- 1$ out of $- (32 z) - 1 (281)$ .

$\frac{- (32 z + 281)}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Simplify the expression.

Rewrite $- (32 z + 281)$ as $- 1 (32 z + 281)$ .

$\frac{- 1 (32 z + 281)}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Move the negative in front of the fraction.

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - 2 x + z$

Replace all occurrences of $x$ in $y = 9 - 2 x + z$ with $\frac{59}{9} + \frac{8 z}{9}$ .

$y = 9 - 2 (\frac{59}{9} + \frac{8 z}{9}) + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Simplify the right side.

Simplify $9 - 2 (\frac{59}{9} + \frac{8 z}{9}) + z$ .

Simplify each term.

Apply the distributive property.

$y = 9 - 2 (\frac{59}{9}) - 2 \frac{8 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Multiply $- 2 (\frac{59}{9})$ .

Combine $- 2$ and $\frac{59}{9}$ .

$y = 9 + \frac{- 2 \cdot 59}{9} - 2 \frac{8 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Multiply $- 2$ by $59$ .

$y = 9 + \frac{- 118}{9} - 2 \frac{8 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 + \frac{- 118}{9} - 2 \frac{8 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Multiply $- 2 \frac{8 z}{9}$ .

Combine $- 2$ and $\frac{8 z}{9}$ .

$y = 9 + \frac{- 118}{9} + \frac{- 2 (8 z)}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Multiply $8$ by $- 2$ .

$y = 9 + \frac{- 118}{9} + \frac{- 16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 + \frac{- 118}{9} + \frac{- 16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Simplify each term.

Move the negative in front of the fraction.

$y = 9 - \frac{118}{9} + \frac{- 16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Move the negative in front of the fraction.

$y = 9 - \frac{118}{9} - \frac{16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - \frac{118}{9} - \frac{16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = 9 - \frac{118}{9} - \frac{16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

To write $9$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = 9 \cdot \frac{9}{9} - \frac{118}{9} - \frac{16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

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

$y = \frac{9 \cdot 9}{9} - \frac{118}{9} - \frac{16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Combine the numerators over the common denominator.

$y = \frac{9 \cdot 9 - 118}{9} - \frac{16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Simplify the numerator.

Multiply $9$ by $9$ .

$y = \frac{81 - 118}{9} - \frac{16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Subtract $118$ from $81$ .

$y = \frac{- 37}{9} - \frac{16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = \frac{- 37}{9} - \frac{16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Move the negative in front of the fraction.

$y = - \frac{37}{9} - \frac{16 z}{9} + z$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

To write $z$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = - \frac{37}{9} - \frac{16 z}{9} + z \cdot \frac{9}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Simplify terms.

Combine $z$ and $\frac{9}{9}$ .

$y = - \frac{37}{9} - \frac{16 z}{9} + \frac{z \cdot 9}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Combine the numerators over the common denominator.

$y = - \frac{37}{9} + \frac{- 16 z + z \cdot 9}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Combine the numerators over the common denominator.

$y = \frac{- 37 - 16 z + z \cdot 9}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = \frac{- 37 - 16 z + z \cdot 9}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Move $9$ to the left of $z$ .

$y = \frac{- 37 - 16 z + 9 z}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Simplify terms.

Add $- 16 z$ and $9 z$ .

$y = \frac{- 37 - 7 z}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Rewrite $- 37$ as $- 1 (37)$ .

$y = \frac{- 1 \cdot 37 - 7 z}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Factor $- 1$ out of $- 7 z$ .

$y = \frac{- 1 \cdot 37 - (7 z)}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Factor $- 1$ out of $- 1 (37) - (7 z)$ .

$y = \frac{- 1 (37 + 7 z)}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Move the negative in front of the fraction.

$y = - \frac{37 + 7 z}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = - \frac{37 + 7 z}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = - \frac{37 + 7 z}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = - \frac{37 + 7 z}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = - \frac{37 + 7 z}{9}$

$- \frac{32 z + 281}{9} = - 17$

$x = \frac{59}{9} + \frac{8 z}{9}$

Solve for $z$ in $- \frac{32 z + 281}{9} = - 17$ .

Multiply both sides of the equation by $- 9$ .

$- 9 (- \frac{32 z + 281}{9}) = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 9 (- \frac{32 z + 281}{9})$ .

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{32 z + 281}{9}$ into the numerator.

$- 9 \frac{- (32 z + 281)}{9} = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Factor $9$ out of $- 9$ .

$9 (- 1) (\frac{- (32 z + 281)}{9}) = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Cancel the common factor.

$9 \cdot (- 1 \frac{- (32 z + 281)}{9}) = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Rewrite the expression.

$32 z + 281 = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$32 z + 281 = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (32 z + 281) = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Multiply $32 z + 281$ by $1$ .

$32 z + 281 = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$32 z + 281 = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$32 z + 281 = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$32 z + 281 = - 9 \cdot - 17$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Simplify the right side.

Multiply $- 9$ by $- 17$ .

$32 z + 281 = 153$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$32 z + 281 = 153$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$32 z + 281 = 153$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

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

Subtract $281$ from both sides of the equation.

$32 z = 153 - 281$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Subtract $281$ from $153$ .

$32 z = - 128$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$32 z = - 128$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Divide each term in $32 z = - 128$ by $32$ and simplify.

Divide each term in $32 z = - 128$ by $32$ .

$\frac{32 z}{32} = \frac{- 128}{32}$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Simplify the left side.

Cancel the common factor of $32$ .

Cancel the common factor.

$\frac{32 z}{32} = \frac{- 128}{32}$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Divide $z$ by $1$ .

$z = \frac{- 128}{32}$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$z = \frac{- 128}{32}$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$z = \frac{- 128}{32}$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

Simplify the right side.

Divide $- 128$ by $32$ .

$z = - 4$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$z = - 4$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$z = - 4$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

$z = - 4$

$y = - \frac{37 + 7 z}{9}$

$x = \frac{59}{9} + \frac{8 z}{9}$

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

Replace all occurrences of $z$ in $y = - \frac{37 + 7 z}{9}$ with $- 4$ .

$y = - \frac{37 + 7 (- 4)}{9}$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

Simplify the right side.

Simplify $- \frac{37 + 7 (- 4)}{9}$ .

Simplify the numerator.

Multiply $7$ by $- 4$ .

$y = - \frac{37 - 28}{9}$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

Subtract $28$ from $37$ .

$y = - \frac{9}{9}$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = - \frac{9}{9}$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $9$ .

Cancel the common factor.

$y = - \frac{9}{9}$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

Rewrite the expression.

$y = - 1 \cdot 1$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = - 1 \cdot 1$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

Multiply $- 1$ by $1$ .

$y = - 1$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = - 1$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = - 1$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

$y = - 1$

$z = - 4$

$x = \frac{59}{9} + \frac{8 z}{9}$

Replace all occurrences of $z$ in $x = \frac{59}{9} + \frac{8 z}{9}$ with $- 4$ .

$x = \frac{59}{9} + \frac{8 (- 4)}{9}$

$y = - 1$

$z = - 4$

Simplify the right side.

Simplify $\frac{59}{9} + \frac{8 (- 4)}{9}$ .

Combine the numerators over the common denominator.

$x = \frac{59 + 8 (- 4)}{9}$

$y = - 1$

$z = - 4$

Simplify the expression.

Multiply $8$ by $- 4$ .

$x = \frac{59 - 32}{9}$

$y = - 1$

$z = - 4$

Subtract $32$ from $59$ .

$x = \frac{27}{9}$

$y = - 1$

$z = - 4$

Divide $27$ by $9$ .

$x = 3$

$y = - 1$

$z = - 4$

$x = 3$

$y = - 1$

$z = - 4$

$x = 3$

$y = - 1$

$z = - 4$

$x = 3$

$y = - 1$

$z = - 4$

$x = 3$

$y = - 1$

$z = - 4$

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

$(3, - 1, - 4)$

The result can be shown in multiple forms.

Point Form:

$(3, - 1, - 4)$

Equation Form:

$x = 3, y = - 1, z = - 4$

Solve the System of Equations 2x+y-z=9 -x+6y+2z=-17 5x+7y+z=4

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