Solve the System of Equations -6x-2y-z=-17 5x+y-6z=19 -4x-6y-6z=-20

$- 6 x - 2 y - z = - 17$ $5 x + y - 6 z = 19$ $- 4 x - 6 y - 6 z = - 20$

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

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

$y - 6 z = 19 - 5 x$

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

$- 4 x - 6 y - 6 z = - 20$

Add $6 z$ to both sides of the equation.

$y = 19 - 5 x + 6 z$

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

$- 4 x - 6 y - 6 z = - 20$

$y = 19 - 5 x + 6 z$

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

$- 4 x - 6 y - 6 z = - 20$

Replace all occurrences of $y$ with $19 - 5 x + 6 z$ in each equation.

Replace all occurrences of $y$ in $- 6 x - 2 y - z = - 17$ with $19 - 5 x + 6 z$ .

$- 6 x - 2 (19 - 5 x + 6 z) - z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

Simplify the left side.

Simplify $- 6 x - 2 (19 - 5 x + 6 z) - z$ .

Simplify each term.

Apply the distributive property.

$- 6 x - 2 \cdot 19 - 2 (- 5 x) - 2 (6 z) - z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

Simplify.

Multiply $- 2$ by $19$ .

$- 6 x - 38 - 2 (- 5 x) - 2 (6 z) - z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

Multiply $- 5$ by $- 2$ .

$- 6 x - 38 + 10 x - 2 (6 z) - z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

Multiply $6$ by $- 2$ .

$- 6 x - 38 + 10 x - 12 z - z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

$- 6 x - 38 + 10 x - 12 z - z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

$- 6 x - 38 + 10 x - 12 z - z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

Simplify by adding terms.

Add $- 6 x$ and $10 x$ .

$4 x - 38 - 12 z - z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

Subtract $z$ from $- 12 z$ .

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 6 y - 6 z = - 20$

Replace all occurrences of $y$ in $- 4 x - 6 y - 6 z = - 20$ with $19 - 5 x + 6 z$ .

$- 4 x - 6 (19 - 5 x + 6 z) - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Simplify the left side.

Simplify $- 4 x - 6 (19 - 5 x + 6 z) - 6 z$ .

Simplify each term.

Apply the distributive property.

$- 4 x - 6 \cdot 19 - 6 (- 5 x) - 6 (6 z) - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Simplify.

Multiply $- 6$ by $19$ .

$- 4 x - 114 - 6 (- 5 x) - 6 (6 z) - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Multiply $- 5$ by $- 6$ .

$- 4 x - 114 + 30 x - 6 (6 z) - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Multiply $6$ by $- 6$ .

$- 4 x - 114 + 30 x - 36 z - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 114 + 30 x - 36 z - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$- 4 x - 114 + 30 x - 36 z - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Simplify by adding terms.

Add $- 4 x$ and $30 x$ .

$26 x - 114 - 36 z - 6 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Subtract $6 z$ from $- 36 z$ .

$26 x - 114 - 42 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$26 x - 114 - 42 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$26 x - 114 - 42 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$26 x - 114 - 42 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$26 x - 114 - 42 z = - 20$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Solve for $x$ in $26 x - 114 - 42 z = - 20$ .

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

Add $114$ to both sides of the equation.

$26 x - 42 z = - 20 + 114$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Add $42 z$ to both sides of the equation.

$26 x = - 20 + 114 + 42 z$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Add $- 20$ and $114$ .

$26 x = 94 + 42 z$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$26 x = 94 + 42 z$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Divide each term in $26 x = 94 + 42 z$ by $26$ and simplify.

Divide each term in $26 x = 94 + 42 z$ by $26$ .

$\frac{26 x}{26} = \frac{94}{26} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 x}{26} = \frac{94}{26} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Divide $x$ by $1$ .

$x = \frac{94}{26} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$x = \frac{94}{26} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$x = \frac{94}{26} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Simplify the right side.

Simplify each term.

Cancel the common factor of $94$ and $26$ .

Factor $2$ out of $94$ .

$x = \frac{2 (47)}{26} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Cancel the common factors.

Factor $2$ out of $26$ .

$x = \frac{2 \cdot 47}{2 \cdot 13} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Cancel the common factor.

$x = \frac{2 \cdot 47}{2 \cdot 13} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Rewrite the expression.

$x = \frac{47}{13} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$x = \frac{47}{13} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$x = \frac{47}{13} + \frac{42 z}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Cancel the common factor of $42$ and $26$ .

Factor $2$ out of $42 z$ .

$x = \frac{47}{13} + \frac{2 (21 z)}{26}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Cancel the common factors.

Factor $2$ out of $26$ .

$x = \frac{47}{13} + \frac{2 (21 z)}{2 (13)}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Cancel the common factor.

$x = \frac{47}{13} + \frac{2 (21 z)}{2 \cdot 13}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Rewrite the expression.

$x = \frac{47}{13} + \frac{21 z}{13}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$x = \frac{47}{13} + \frac{21 z}{13}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$x = \frac{47}{13} + \frac{21 z}{13}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$x = \frac{47}{13} + \frac{21 z}{13}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$x = \frac{47}{13} + \frac{21 z}{13}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$x = \frac{47}{13} + \frac{21 z}{13}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

$x = \frac{47}{13} + \frac{21 z}{13}$

$4 x - 38 - 13 z = - 17$

$y = 19 - 5 x + 6 z$

Replace all occurrences of $x$ with $\frac{47}{13} + \frac{21 z}{13}$ in each equation.

Replace all occurrences of $x$ in $4 x - 38 - 13 z = - 17$ with $\frac{47}{13} + \frac{21 z}{13}$ .

$4 (\frac{47}{13} + \frac{21 z}{13}) - 38 - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Simplify the left side.

Simplify $4 (\frac{47}{13} + \frac{21 z}{13}) - 38 - 13 z$ .

Simplify each term.

Apply the distributive property.

$4 (\frac{47}{13}) + 4 (\frac{21 z}{13}) - 38 - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Multiply $4 (\frac{47}{13})$ .

Combine $4$ and $\frac{47}{13}$ .

$\frac{4 \cdot 47}{13} + 4 (\frac{21 z}{13}) - 38 - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Multiply $4$ by $47$ .

$\frac{188}{13} + 4 (\frac{21 z}{13}) - 38 - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

$\frac{188}{13} + 4 (\frac{21 z}{13}) - 38 - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Multiply $4 \frac{21 z}{13}$ .

Combine $4$ and $\frac{21 z}{13}$ .

$\frac{188}{13} + \frac{4 (21 z)}{13} - 38 - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Multiply $21$ by $4$ .

$\frac{188}{13} + \frac{84 z}{13} - 38 - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

$\frac{188}{13} + \frac{84 z}{13} - 38 - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

$\frac{188}{13} + \frac{84 z}{13} - 38 - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

To write $- 38$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$\frac{84 z}{13} + \frac{188}{13} - 38 \cdot \frac{13}{13} - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Combine $- 38$ and $\frac{13}{13}$ .

$\frac{84 z}{13} + \frac{188}{13} + \frac{- 38 \cdot 13}{13} - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Combine the numerators over the common denominator.

$\frac{84 z}{13} + \frac{188 - 38 \cdot 13}{13} - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Simplify the numerator.

Multiply $- 38$ by $13$ .

$\frac{84 z}{13} + \frac{188 - 494}{13} - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Subtract $494$ from $188$ .

$\frac{84 z}{13} + \frac{- 306}{13} - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

$\frac{84 z}{13} + \frac{- 306}{13} - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Move the negative in front of the fraction.

$\frac{84 z}{13} - \frac{306}{13} - 13 z = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

To write $- 13 z$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$\frac{84 z}{13} - 13 z \cdot \frac{13}{13} - \frac{306}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

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

$\frac{84 z}{13} + \frac{- 13 z \cdot 13}{13} - \frac{306}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Combine the numerators over the common denominator.

$\frac{84 z - 13 z \cdot 13}{13} - \frac{306}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Combine the numerators over the common denominator.

$\frac{84 z - 13 z \cdot 13 - 306}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Multiply $13$ by $- 13$ .

$\frac{84 z - 169 z - 306}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Subtract $169 z$ from $84 z$ .

$\frac{- 85 z - 306}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Factor $17$ out of $- 85 z - 306$ .

Factor $17$ out of $- 85 z$ .

$\frac{17 (- 5 z) - 306}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Factor $17$ out of $- 306$ .

$\frac{17 (- 5 z) + 17 (- 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Factor $17$ out of $17 (- 5 z) + 17 (- 18)$ .

$\frac{17 (- 5 z - 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

$\frac{17 (- 5 z - 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

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

$\frac{17 (- (5 z) - 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Rewrite $- 18$ as $- 1 (18)$ .

$\frac{17 (- (5 z) - 1 \cdot 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Factor $- 1$ out of $- (5 z) - 1 (18)$ .

$\frac{17 (- (5 z + 18))}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Simplify the expression.

Rewrite $- (5 z + 18)$ as $- 1 (5 z + 18)$ .

$\frac{17 (- 1 (5 z + 18))}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Move the negative in front of the fraction.

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - 5 x + 6 z$

Replace all occurrences of $x$ in $y = 19 - 5 x + 6 z$ with $\frac{47}{13} + \frac{21 z}{13}$ .

$y = 19 - 5 (\frac{47}{13} + \frac{21 z}{13}) + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Simplify the right side.

Simplify $19 - 5 (\frac{47}{13} + \frac{21 z}{13}) + 6 z$ .

Simplify each term.

Apply the distributive property.

$y = 19 - 5 (\frac{47}{13}) - 5 \frac{21 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Multiply $- 5 (\frac{47}{13})$ .

Combine $- 5$ and $\frac{47}{13}$ .

$y = 19 + \frac{- 5 \cdot 47}{13} - 5 \frac{21 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Multiply $- 5$ by $47$ .

$y = 19 + \frac{- 235}{13} - 5 \frac{21 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 + \frac{- 235}{13} - 5 \frac{21 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Multiply $- 5 \frac{21 z}{13}$ .

Combine $- 5$ and $\frac{21 z}{13}$ .

$y = 19 + \frac{- 235}{13} + \frac{- 5 (21 z)}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Multiply $21$ by $- 5$ .

$y = 19 + \frac{- 235}{13} + \frac{- 105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 + \frac{- 235}{13} + \frac{- 105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Simplify each term.

Move the negative in front of the fraction.

$y = 19 - \frac{235}{13} + \frac{- 105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Move the negative in front of the fraction.

$y = 19 - \frac{235}{13} - \frac{105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - \frac{235}{13} - \frac{105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 19 - \frac{235}{13} - \frac{105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

To write $19$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$y = 19 \cdot \frac{13}{13} - \frac{235}{13} - \frac{105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Combine $19$ and $\frac{13}{13}$ .

$y = \frac{19 \cdot 13}{13} - \frac{235}{13} - \frac{105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Combine the numerators over the common denominator.

$y = \frac{19 \cdot 13 - 235}{13} - \frac{105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Simplify the numerator.

Multiply $19$ by $13$ .

$y = \frac{247 - 235}{13} - \frac{105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Subtract $235$ from $247$ .

$y = \frac{12}{13} - \frac{105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = \frac{12}{13} - \frac{105 z}{13} + 6 z$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

To write $6 z$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$y = \frac{12}{13} - \frac{105 z}{13} + 6 z \cdot \frac{13}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Combine $6 z$ and $\frac{13}{13}$ .

$y = \frac{12}{13} - \frac{105 z}{13} + \frac{6 z \cdot 13}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Combine the numerators over the common denominator.

$y = \frac{12}{13} + \frac{- 105 z + 6 z \cdot 13}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Combine the numerators over the common denominator.

$y = \frac{12 - 105 z + 6 z \cdot 13}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Multiply $13$ by $6$ .

$y = \frac{12 - 105 z + 78 z}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Add $- 105 z$ and $78 z$ .

$y = \frac{12 - 27 z}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Factor $3$ out of $12 - 27 z$ .

Factor $3$ out of $12$ .

$y = \frac{3 (4) - 27 z}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Factor $3$ out of $- 27 z$ .

$y = \frac{3 (4) + 3 (- 9 z)}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Factor $3$ out of $3 (4) + 3 (- 9 z)$ .

$y = \frac{3 (4 - 9 z)}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = \frac{3 (4 - 9 z)}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = \frac{3 (4 - 9 z)}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = \frac{3 (4 - 9 z)}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = \frac{3 (4 - 9 z)}{13}$

$- \frac{17 (5 z + 18)}{13} = - 17$

$x = \frac{47}{13} + \frac{21 z}{13}$

Solve for $z$ in $- \frac{17 (5 z + 18)}{13} = - 17$ .

Multiply both sides of the equation by $- \frac{13}{17}$ .

$- \frac{13}{17} \cdot (- \frac{17 (5 z + 18)}{13}) = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{13}{17} (- \frac{17 (5 z + 18)}{13})$ .

Cancel the common factor of $13$ .

Move the leading negative in $- \frac{13}{17}$ into the numerator.

$\frac{- 13}{17} \cdot (- \frac{17 (5 z + 18)}{13}) = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Move the leading negative in $- \frac{17 (5 z + 18)}{13}$ into the numerator.

$\frac{- 13}{17} \cdot \frac{- 17 (5 z + 18)}{13} = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Factor $13$ out of $- 13$ .

$\frac{13 (- 1)}{17} \cdot \frac{- 17 (5 z + 18)}{13} = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Cancel the common factor.

$\frac{13 \cdot - 1}{17} \cdot \frac{- 17 (5 z + 18)}{13} = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Rewrite the expression.

$\frac{- 1}{17} \cdot (- 17 (5 z + 18)) = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$\frac{- 1}{17} \cdot (- 17 (5 z + 18)) = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Cancel the common factor of $17$ .

Factor $17$ out of $- 17 (5 z + 18)$ .

$\frac{- 1}{17} \cdot (17 (- (5 z + 18))) = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Cancel the common factor.

$\frac{- 1}{17} \cdot (17 (- (5 z + 18))) = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Rewrite the expression.

$5 z + 18 = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$5 z + 18 = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (5 z + 18) = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Multiply $5 z + 18$ by $1$ .

$5 z + 18 = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$5 z + 18 = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$5 z + 18 = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$5 z + 18 = - \frac{13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Simplify the right side.

Simplify $- \frac{13}{17} \cdot - 17$ .

Cancel the common factor of $17$ .

Move the leading negative in $- \frac{13}{17}$ into the numerator.

$5 z + 18 = \frac{- 13}{17} \cdot - 17$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Factor $17$ out of $- 17$ .

$5 z + 18 = \frac{- 13}{17} \cdot (17 (- 1))$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Cancel the common factor.

$5 z + 18 = \frac{- 13}{17} \cdot (17 \cdot - 1)$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Rewrite the expression.

$5 z + 18 = - 13 \cdot - 1$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$5 z + 18 = - 13 \cdot - 1$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Multiply $- 13$ by $- 1$ .

$5 z + 18 = 13$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$5 z + 18 = 13$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$5 z + 18 = 13$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$5 z + 18 = 13$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

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

Subtract $18$ from both sides of the equation.

$5 z = 13 - 18$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Subtract $18$ from $13$ .

$5 z = - 5$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$5 z = - 5$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

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

Divide each term in $5 z = - 5$ by $5$ .

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

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Divide $z$ by $1$ .

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

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

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

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

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

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

Simplify the right side.

Divide $- 5$ by $5$ .

$z = - 1$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$z = - 1$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$z = - 1$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

$z = - 1$

$y = \frac{3 (4 - 9 z)}{13}$

$x = \frac{47}{13} + \frac{21 z}{13}$

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

Replace all occurrences of $z$ in $y = \frac{3 (4 - 9 z)}{13}$ with $- 1$ .

$y = \frac{3 (4 - 9 \cdot - 1)}{13}$

$z = - 1$

$x = \frac{47}{13} + \frac{21 z}{13}$

Simplify the right side.

Simplify $\frac{3 (4 - 9 \cdot - 1)}{13}$ .

Simplify the numerator.

Multiply $- 9$ by $- 1$ .

$y = \frac{3 (4 + 9)}{13}$

$z = - 1$

$x = \frac{47}{13} + \frac{21 z}{13}$

Add $4$ and $9$ .

$y = \frac{3 \cdot 13}{13}$

$z = - 1$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = \frac{3 \cdot 13}{13}$

$z = - 1$

$x = \frac{47}{13} + \frac{21 z}{13}$

Simplify the expression.

Multiply $3$ by $13$ .

$y = \frac{39}{13}$

$z = - 1$

$x = \frac{47}{13} + \frac{21 z}{13}$

Divide $39$ by $13$ .

$y = 3$

$z = - 1$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 3$

$z = - 1$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 3$

$z = - 1$

$x = \frac{47}{13} + \frac{21 z}{13}$

$y = 3$

$z = - 1$

$x = \frac{47}{13} + \frac{21 z}{13}$

Replace all occurrences of $z$ in $x = \frac{47}{13} + \frac{21 z}{13}$ with $- 1$ .

$x = \frac{47}{13} + \frac{21 (- 1)}{13}$

$y = 3$

$z = - 1$

Simplify the right side.

Simplify $\frac{47}{13} + \frac{21 (- 1)}{13}$ .

Combine the numerators over the common denominator.

$x = \frac{47 + 21 (- 1)}{13}$

$y = 3$

$z = - 1$

Simplify the expression.

Multiply $21$ by $- 1$ .

$x = \frac{47 - 21}{13}$

$y = 3$

$z = - 1$

Subtract $21$ from $47$ .

$x = \frac{26}{13}$

$y = 3$

$z = - 1$

Divide $26$ by $13$ .

$x = 2$

$y = 3$

$z = - 1$

$x = 2$

$y = 3$

$z = - 1$

$x = 2$

$y = 3$

$z = - 1$

$x = 2$

$y = 3$

$z = - 1$

$x = 2$

$y = 3$

$z = - 1$

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

$(2, 3, - 1)$

The result can be shown in multiple forms.

Point Form:

$(2, 3, - 1)$

Equation Form:

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

Solve the System of Equations -6x-2y-z=-17 5x+y-6z=19 -4x-6y-6z=-20

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