Solve the System of Equations 5x-4y-6z=-3 x-3y+z=-1 -3x-6y+7z=1

$5 x - 4 y - 6 z = - 3$ $x - 3 y + z = - 1$ $- 3 x - 6 y + 7 z = 1$

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

Add $3 y$ to both sides of the equation.

$x + z = - 1 + 3 y$

$5 x - 4 y - 6 z = - 3$

$- 3 x - 6 y + 7 z = 1$

Subtract $z$ from both sides of the equation.

$x = - 1 + 3 y - z$

$5 x - 4 y - 6 z = - 3$

$- 3 x - 6 y + 7 z = 1$

$x = - 1 + 3 y - z$

$5 x - 4 y - 6 z = - 3$

$- 3 x - 6 y + 7 z = 1$

Replace all occurrences of $x$ with $- 1 + 3 y - z$ in each equation.

Replace all occurrences of $x$ in $5 x - 4 y - 6 z = - 3$ with $- 1 + 3 y - z$ .

$5 (- 1 + 3 y - z) - 4 y - 6 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

Simplify the left side.

Simplify $5 (- 1 + 3 y - z) - 4 y - 6 z$ .

Simplify each term.

Apply the distributive property.

$5 \cdot - 1 + 5 (3 y) + 5 (- z) - 4 y - 6 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

Simplify.

Multiply $5$ by $- 1$ .

$- 5 + 5 (3 y) + 5 (- z) - 4 y - 6 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

Multiply $3$ by $5$ .

$- 5 + 15 y + 5 (- z) - 4 y - 6 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

Multiply $- 1$ by $5$ .

$- 5 + 15 y - 5 z - 4 y - 6 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

$- 5 + 15 y - 5 z - 4 y - 6 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

$- 5 + 15 y - 5 z - 4 y - 6 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

Simplify by adding terms.

Subtract $4 y$ from $15 y$ .

$- 5 + 11 y - 5 z - 6 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

Subtract $6 z$ from $- 5 z$ .

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$- 3 x - 6 y + 7 z = 1$

Replace all occurrences of $x$ in $- 3 x - 6 y + 7 z = 1$ with $- 1 + 3 y - z$ .

$- 3 (- 1 + 3 y - z) - 6 y + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Simplify the left side.

Simplify $- 3 (- 1 + 3 y - z) - 6 y + 7 z$ .

Simplify each term.

Apply the distributive property.

$- 3 \cdot - 1 - 3 (3 y) - 3 (- z) - 6 y + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Simplify.

Multiply $- 3$ by $- 1$ .

$3 - 3 (3 y) - 3 (- z) - 6 y + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Multiply $3$ by $- 3$ .

$3 - 9 y - 3 (- z) - 6 y + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Multiply $- 1$ by $- 3$ .

$3 - 9 y + 3 z - 6 y + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$3 - 9 y + 3 z - 6 y + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$3 - 9 y + 3 z - 6 y + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Simplify by adding terms.

Subtract $6 y$ from $- 9 y$ .

$3 - 15 y + 3 z + 7 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Add $3 z$ and $7 z$ .

$3 - 15 y + 10 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$3 - 15 y + 10 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$3 - 15 y + 10 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$3 - 15 y + 10 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$3 - 15 y + 10 z = 1$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Solve for $y$ in $3 - 15 y + 10 z = 1$ .

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

Subtract $3$ from both sides of the equation.

$- 15 y + 10 z = 1 - 3$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Subtract $10 z$ from both sides of the equation.

$- 15 y = 1 - 3 - 10 z$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Subtract $3$ from $1$ .

$- 15 y = - 2 - 10 z$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$- 15 y = - 2 - 10 z$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Divide each term in $- 15 y = - 2 - 10 z$ by $- 15$ and simplify.

Divide each term in $- 15 y = - 2 - 10 z$ by $- 15$ .

$\frac{- 15 y}{- 15} = \frac{- 2}{- 15} + \frac{- 10 z}{- 15}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 y}{- 15} = \frac{- 2}{- 15} + \frac{- 10 z}{- 15}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Divide $y$ by $1$ .

$y = \frac{- 2}{- 15} + \frac{- 10 z}{- 15}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$y = \frac{- 2}{- 15} + \frac{- 10 z}{- 15}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$y = \frac{- 2}{- 15} + \frac{- 10 z}{- 15}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{2}{15} + \frac{- 10 z}{- 15}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Cancel the common factor of $- 10$ and $- 15$ .

Factor $- 5$ out of $- 10 z$ .

$y = \frac{2}{15} + \frac{- 5 (2 z)}{- 15}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Cancel the common factors.

Factor $- 5$ out of $- 15$ .

$y = \frac{2}{15} + \frac{- 5 (2 z)}{- 5 \cdot 3}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Cancel the common factor.

$y = \frac{2}{15} + \frac{- 5 (2 z)}{- 5 \cdot 3}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Rewrite the expression.

$y = \frac{2}{15} + \frac{2 z}{3}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$y = \frac{2}{15} + \frac{2 z}{3}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$y = \frac{2}{15} + \frac{2 z}{3}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$y = \frac{2}{15} + \frac{2 z}{3}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$y = \frac{2}{15} + \frac{2 z}{3}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$y = \frac{2}{15} + \frac{2 z}{3}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

$y = \frac{2}{15} + \frac{2 z}{3}$

$- 5 + 11 y - 11 z = - 3$

$x = - 1 + 3 y - z$

Replace all occurrences of $y$ with $\frac{2}{15} + \frac{2 z}{3}$ in each equation.

Replace all occurrences of $y$ in $- 5 + 11 y - 11 z = - 3$ with $\frac{2}{15} + \frac{2 z}{3}$ .

$- 5 + 11 (\frac{2}{15} + \frac{2 z}{3}) - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Simplify the left side.

Simplify $- 5 + 11 (\frac{2}{15} + \frac{2 z}{3}) - 11 z$ .

Simplify each term.

Apply the distributive property.

$- 5 + 11 (\frac{2}{15}) + 11 (\frac{2 z}{3}) - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Multiply $11 (\frac{2}{15})$ .

Combine $11$ and $\frac{2}{15}$ .

$- 5 + \frac{11 \cdot 2}{15} + 11 (\frac{2 z}{3}) - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Multiply $11$ by $2$ .

$- 5 + \frac{22}{15} + 11 (\frac{2 z}{3}) - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

$- 5 + \frac{22}{15} + 11 (\frac{2 z}{3}) - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Multiply $11 \frac{2 z}{3}$ .

Combine $11$ and $\frac{2 z}{3}$ .

$- 5 + \frac{22}{15} + \frac{11 (2 z)}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Multiply $2$ by $11$ .

$- 5 + \frac{22}{15} + \frac{22 z}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

$- 5 + \frac{22}{15} + \frac{22 z}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

$- 5 + \frac{22}{15} + \frac{22 z}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$- 5 \cdot \frac{15}{15} + \frac{22}{15} + \frac{22 z}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Combine $- 5$ and $\frac{15}{15}$ .

$\frac{- 5 \cdot 15}{15} + \frac{22}{15} + \frac{22 z}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Combine the numerators over the common denominator.

$\frac{- 5 \cdot 15 + 22}{15} + \frac{22 z}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Simplify the numerator.

Multiply $- 5$ by $15$ .

$\frac{- 75 + 22}{15} + \frac{22 z}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Add $- 75$ and $22$ .

$\frac{- 53}{15} + \frac{22 z}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

$\frac{- 53}{15} + \frac{22 z}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Move the negative in front of the fraction.

$- \frac{53}{15} + \frac{22 z}{3} - 11 z = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

To write $- 11 z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{53}{15} + \frac{22 z}{3} - 11 z \cdot \frac{3}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Simplify terms.

Combine $- 11 z$ and $\frac{3}{3}$ .

$- \frac{53}{15} + \frac{22 z}{3} + \frac{- 11 z \cdot 3}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Combine the numerators over the common denominator.

$- \frac{53}{15} + \frac{22 z - 11 z \cdot 3}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

$- \frac{53}{15} + \frac{22 z - 11 z \cdot 3}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Simplify each term.

Simplify the numerator.

Factor $11 z$ out of $22 z - 11 z \cdot 3$ .

Factor $11 z$ out of $22 z$ .

$- \frac{53}{15} + \frac{11 z (2) - 11 z \cdot 3}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Factor $11 z$ out of $- 11 z \cdot 3$ .

$- \frac{53}{15} + \frac{11 z (2) + 11 z (- 1 \cdot 3)}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Factor $11 z$ out of $11 z (2) + 11 z (- 1 \cdot 3)$ .

$- \frac{53}{15} + \frac{11 z (2 - 1 \cdot 3)}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

$- \frac{53}{15} + \frac{11 z (2 - 1 \cdot 3)}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Multiply $- 1$ by $3$ .

$- \frac{53}{15} + \frac{11 z (2 - 3)}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Subtract $3$ from $2$ .

$- \frac{53}{15} + \frac{11 z \cdot - 1}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Multiply $- 1$ by $11$ .

$- \frac{53}{15} + \frac{- 11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

$- \frac{53}{15} + \frac{- 11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Move the negative in front of the fraction.

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + 3 y - z$

Replace all occurrences of $y$ in $x = - 1 + 3 y - z$ with $\frac{2}{15} + \frac{2 z}{3}$ .

$x = - 1 + 3 (\frac{2}{15} + \frac{2 z}{3}) - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Simplify the right side.

Simplify $- 1 + 3 (\frac{2}{15} + \frac{2 z}{3}) - z$ .

Simplify each term.

Apply the distributive property.

$x = - 1 + 3 (\frac{2}{15}) + 3 (\frac{2 z}{3}) - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$x = - 1 + 3 (\frac{2}{3 (5)}) + 3 (\frac{2 z}{3}) - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Cancel the common factor.

$x = - 1 + 3 (\frac{2}{3 \cdot 5}) + 3 (\frac{2 z}{3}) - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Rewrite the expression.

$x = - 1 + \frac{2}{5} + 3 (\frac{2 z}{3}) - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - 1 + \frac{2}{5} + 3 (\frac{2 z}{3}) - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x = - 1 + \frac{2}{5} + 3 (\frac{2 z}{3}) - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Rewrite the expression.

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

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

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

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

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

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = - 1 \cdot \frac{5}{5} + \frac{2}{5} + 2 z - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

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

$x = \frac{- 1 \cdot 5}{5} + \frac{2}{5} + 2 z - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Combine the numerators over the common denominator.

$x = \frac{- 1 \cdot 5 + 2}{5} + 2 z - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Simplify the numerator.

Multiply $- 1$ by $5$ .

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

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Add $- 5$ and $2$ .

$x = \frac{- 3}{5} + 2 z - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = \frac{- 3}{5} + 2 z - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Move the negative in front of the fraction.

$x = - \frac{3}{5} + 2 z - z$

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Subtract $z$ from $2 z$ .

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

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

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

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

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

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

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

$- \frac{53}{15} - \frac{11 z}{3} = - 3$

$y = \frac{2}{15} + \frac{2 z}{3}$

Solve for $z$ in $- \frac{53}{15} - \frac{11 z}{3} = - 3$ .

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

Add $\frac{53}{15}$ to both sides of the equation.

$- \frac{11 z}{3} = - 3 + \frac{53}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$- \frac{11 z}{3} = - 3 \cdot \frac{15}{15} + \frac{53}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Combine $- 3$ and $\frac{15}{15}$ .

$- \frac{11 z}{3} = \frac{- 3 \cdot 15}{15} + \frac{53}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Combine the numerators over the common denominator.

$- \frac{11 z}{3} = \frac{- 3 \cdot 15 + 53}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Simplify the numerator.

Multiply $- 3$ by $15$ .

$- \frac{11 z}{3} = \frac{- 45 + 53}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Add $- 45$ and $53$ .

$- \frac{11 z}{3} = \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$- \frac{11 z}{3} = \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$- \frac{11 z}{3} = \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Multiply both sides of the equation by $- \frac{3}{11}$ .

$- \frac{3}{11} \cdot (- \frac{11 z}{3}) = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{11} (- \frac{11 z}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{11}$ into the numerator.

$\frac{- 3}{11} \cdot (- \frac{11 z}{3}) = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Move the leading negative in $- \frac{11 z}{3}$ into the numerator.

$\frac{- 3}{11} \cdot \frac{- 11 z}{3} = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{11} \cdot \frac{- 11 z}{3} = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Cancel the common factor.

$\frac{3 \cdot - 1}{11} \cdot \frac{- 11 z}{3} = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Rewrite the expression.

$\frac{- 1}{11} \cdot (- 11 z) = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$\frac{- 1}{11} \cdot (- 11 z) = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Cancel the common factor of $11$ .

Factor $11$ out of $- 11 z$ .

$\frac{- 1}{11} \cdot (11 (- z)) = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Cancel the common factor.

$\frac{- 1}{11} \cdot (11 (- z)) = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Rewrite the expression.

$z = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$z = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Multiply $z$ by $1$ .

$z = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$z = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$z = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$z = - \frac{3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Simplify the right side.

Simplify $- \frac{3}{11} \cdot \frac{8}{15}$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{11}$ into the numerator.

$z = \frac{- 3}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Factor $3$ out of $- 3$ .

$z = \frac{3 (- 1)}{11} \cdot \frac{8}{15}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Factor $3$ out of $15$ .

$z = \frac{3 \cdot - 1}{11} \cdot \frac{8}{3 \cdot 5}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Cancel the common factor.

$z = \frac{3 \cdot - 1}{11} \cdot \frac{8}{3 \cdot 5}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Rewrite the expression.

$z = \frac{- 1}{11} \cdot \frac{8}{5}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$z = \frac{- 1}{11} \cdot \frac{8}{5}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Multiply $\frac{- 1}{11}$ by $\frac{8}{5}$ .

$z = \frac{- 1 \cdot 8}{11 \cdot 5}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Simplify the expression.

Multiply $- 1$ by $8$ .

$z = \frac{- 8}{11 \cdot 5}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Multiply $11$ by $5$ .

$z = \frac{- 8}{55}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Move the negative in front of the fraction.

$z = - \frac{8}{55}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$z = - \frac{8}{55}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$z = - \frac{8}{55}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$z = - \frac{8}{55}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$z = - \frac{8}{55}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

$z = - \frac{8}{55}$

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

$y = \frac{2}{15} + \frac{2 z}{3}$

Replace all occurrences of $z$ with $- \frac{8}{55}$ in each equation.

Replace all occurrences of $z$ in $x = - \frac{3}{5} + z$ with $- \frac{8}{55}$ .

$x = - \frac{3}{5} - \frac{8}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

Simplify $x = - \frac{3}{5} - \frac{8}{55}$ .

Simplify the left side.

Remove parentheses.

$x = - \frac{3}{5} - \frac{8}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - \frac{3}{5} - \frac{8}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

Simplify the right side.

Simplify $- \frac{3}{5} - \frac{8}{55}$ .

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x = - \frac{3}{5} \cdot \frac{11}{11} - \frac{8}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

Write each expression with a common denominator of $55$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{5}$ by $\frac{11}{11}$ .

$x = - \frac{3 \cdot 11}{5 \cdot 11} - \frac{8}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

Multiply $5$ by $11$ .

$x = - \frac{3 \cdot 11}{55} - \frac{8}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - \frac{3 \cdot 11}{55} - \frac{8}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

Combine the numerators over the common denominator.

$x = \frac{- 3 \cdot 11 - 8}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

Simplify the numerator.

Multiply $- 3$ by $11$ .

$x = \frac{- 33 - 8}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

Subtract $8$ from $- 33$ .

$x = \frac{- 41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = \frac{- 41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

Move the negative in front of the fraction.

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{2 z}{3}$

Replace all occurrences of $z$ in $y = \frac{2}{15} + \frac{2 z}{3}$ with $- \frac{8}{55}$ .

$y = \frac{2}{15} + \frac{2 (- \frac{8}{55})}{3}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Simplify the right side.

Simplify $\frac{2}{15} + \frac{2 (- \frac{8}{55})}{3}$ .

Simplify each term.

Simplify the numerator.

Multiply $- 1$ by $2$ .

$y = \frac{2}{15} + \frac{- 2 (\frac{8}{55})}{3}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Combine $- 2$ and $\frac{8}{55}$ .

$y = \frac{2}{15} + \frac{\frac{- 2 \cdot 8}{55}}{3}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} + \frac{\frac{- 2 \cdot 8}{55}}{3}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Multiply $- 2$ by $8$ .

$y = \frac{2}{15} + \frac{\frac{- 16}{55}}{3}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Move the negative in front of the fraction.

$y = \frac{2}{15} + \frac{- \frac{16}{55}}{3}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{2}{15} - \frac{16}{55} \cdot \frac{1}{3}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Multiply $- \frac{16}{55} \cdot \frac{1}{3}$ .

Multiply $\frac{1}{3}$ by $\frac{16}{55}$ .

$y = \frac{2}{15} - \frac{16}{3 \cdot 55}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Multiply $3$ by $55$ .

$y = \frac{2}{15} - \frac{16}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} - \frac{16}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{15} - \frac{16}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

To write $\frac{2}{15}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$y = \frac{2}{15} \cdot \frac{11}{11} - \frac{16}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Write each expression with a common denominator of $165$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{15}$ by $\frac{11}{11}$ .

$y = \frac{2 \cdot 11}{15 \cdot 11} - \frac{16}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Multiply $15$ by $11$ .

$y = \frac{2 \cdot 11}{165} - \frac{16}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2 \cdot 11}{165} - \frac{16}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Combine the numerators over the common denominator.

$y = \frac{2 \cdot 11 - 16}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Simplify the numerator.

Multiply $2$ by $11$ .

$y = \frac{22 - 16}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Subtract $16$ from $22$ .

$y = \frac{6}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{6}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Cancel the common factor of $6$ and $165$ .

Factor $3$ out of $6$ .

$y = \frac{3 (2)}{165}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Cancel the common factors.

Factor $3$ out of $165$ .

$y = \frac{3 \cdot 2}{3 \cdot 55}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Cancel the common factor.

$y = \frac{3 \cdot 2}{3 \cdot 55}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

Rewrite the expression.

$y = \frac{2}{55}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{55}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{55}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{55}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{55}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

$y = \frac{2}{55}$

$x = - \frac{41}{55}$

$z = - \frac{8}{55}$

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

$(- \frac{41}{55}, \frac{2}{55}, - \frac{8}{55})$

The result can be shown in multiple forms.

Point Form:

$(- \frac{41}{55}, \frac{2}{55}, - \frac{8}{55})$

Equation Form:

$x = - \frac{41}{55}, y = \frac{2}{55}, z = - \frac{8}{55}$

Solve the System of Equations 5x-4y-6z=-3 x-3y+z=-1 -3x-6y+7z=1

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