Solve the System of Equations 3x+2y-3z=-2 7x-2y+5z=-14 2x+4y+z=6

$3 x + 2 y - 3 z = - 2$ $7 x - 2 y + 5 z = - 14$ $2 x + 4 y + z = 6$

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

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

$4 y + z = 6 - 2 x$

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

$7 x - 2 y + 5 z = - 14$

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

$z = 6 - 2 x - 4 y$

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

$7 x - 2 y + 5 z = - 14$

$z = 6 - 2 x - 4 y$

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

$7 x - 2 y + 5 z = - 14$

Replace all occurrences of $z$ with $6 - 2 x - 4 y$ in each equation.

Replace all occurrences of $z$ in $3 x + 2 y - 3 z = - 2$ with $6 - 2 x - 4 y$ .

$3 x + 2 y - 3 (6 - 2 x - 4 y) = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

Simplify the left side.

Simplify $3 x + 2 y - 3 (6 - 2 x - 4 y)$ .

Simplify each term.

Apply the distributive property.

$3 x + 2 y - 3 \cdot 6 - 3 (- 2 x) - 3 (- 4 y) = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

Simplify.

Multiply $- 3$ by $6$ .

$3 x + 2 y - 18 - 3 (- 2 x) - 3 (- 4 y) = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

Multiply $- 2$ by $- 3$ .

$3 x + 2 y - 18 + 6 x - 3 (- 4 y) = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

Multiply $- 4$ by $- 3$ .

$3 x + 2 y - 18 + 6 x + 12 y = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

$3 x + 2 y - 18 + 6 x + 12 y = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

$3 x + 2 y - 18 + 6 x + 12 y = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

Simplify by adding terms.

Add $3 x$ and $6 x$ .

$9 x + 2 y - 18 + 12 y = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

Add $2 y$ and $12 y$ .

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 5 z = - 14$

Replace all occurrences of $z$ in $7 x - 2 y + 5 z = - 14$ with $6 - 2 x - 4 y$ .

$7 x - 2 y + 5 (6 - 2 x - 4 y) = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Simplify the left side.

Simplify $7 x - 2 y + 5 (6 - 2 x - 4 y)$ .

Simplify each term.

Apply the distributive property.

$7 x - 2 y + 5 \cdot 6 + 5 (- 2 x) + 5 (- 4 y) = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Simplify.

Multiply $5$ by $6$ .

$7 x - 2 y + 30 + 5 (- 2 x) + 5 (- 4 y) = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Multiply $- 2$ by $5$ .

$7 x - 2 y + 30 - 10 x + 5 (- 4 y) = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Multiply $- 4$ by $5$ .

$7 x - 2 y + 30 - 10 x - 20 y = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 30 - 10 x - 20 y = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$7 x - 2 y + 30 - 10 x - 20 y = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Simplify by adding terms.

Subtract $10 x$ from $7 x$ .

$- 3 x - 2 y + 30 - 20 y = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Subtract $20 y$ from $- 2 y$ .

$- 3 x - 22 y + 30 = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$- 3 x - 22 y + 30 = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$- 3 x - 22 y + 30 = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$- 3 x - 22 y + 30 = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$- 3 x - 22 y + 30 = - 14$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Solve for $x$ in $- 3 x - 22 y + 30 = - 14$ .

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

Add $22 y$ to both sides of the equation.

$- 3 x + 30 = - 14 + 22 y$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Subtract $30$ from both sides of the equation.

$- 3 x = - 14 + 22 y - 30$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Subtract $30$ from $- 14$ .

$- 3 x = 22 y - 44$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$- 3 x = 22 y - 44$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Divide each term in $- 3 x = 22 y - 44$ by $- 3$ and simplify.

Divide each term in $- 3 x = 22 y - 44$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{22 y}{- 3} + \frac{- 44}{- 3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{22 y}{- 3} + \frac{- 44}{- 3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Divide $x$ by $1$ .

$x = \frac{22 y}{- 3} + \frac{- 44}{- 3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$x = \frac{22 y}{- 3} + \frac{- 44}{- 3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$x = \frac{22 y}{- 3} + \frac{- 44}{- 3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{22 y}{3} + \frac{- 44}{- 3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Dividing two negative values results in a positive value.

$x = - \frac{22 y}{3} + \frac{44}{3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$9 x + 14 y - 18 = - 2$

$z = 6 - 2 x - 4 y$

Replace all occurrences of $x$ with $- \frac{22 y}{3} + \frac{44}{3}$ in each equation.

Replace all occurrences of $x$ in $9 x + 14 y - 18 = - 2$ with $- \frac{22 y}{3} + \frac{44}{3}$ .

$9 (- \frac{22 y}{3} + \frac{44}{3}) + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Simplify the left side.

Simplify $9 (- \frac{22 y}{3} + \frac{44}{3}) + 14 y - 18$ .

Simplify each term.

Apply the distributive property.

$9 (- \frac{22 y}{3}) + 9 (\frac{44}{3}) + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{22 y}{3}$ into the numerator.

$9 (\frac{- 22 y}{3}) + 9 (\frac{44}{3}) + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Factor $3$ out of $9$ .

$3 (3) (\frac{- 22 y}{3}) + 9 (\frac{44}{3}) + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Cancel the common factor.

$3 \cdot (3 (\frac{- 22 y}{3})) + 9 (\frac{44}{3}) + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Rewrite the expression.

$3 (- 22 y) + 9 (\frac{44}{3}) + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

$3 (- 22 y) + 9 (\frac{44}{3}) + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Multiply $- 22$ by $3$ .

$- 66 y + 9 (\frac{44}{3}) + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$- 66 y + 3 (3) (\frac{44}{3}) + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Cancel the common factor.

$- 66 y + 3 \cdot (3 (\frac{44}{3})) + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Rewrite the expression.

$- 66 y + 3 \cdot 44 + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

$- 66 y + 3 \cdot 44 + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Multiply $3$ by $44$ .

$- 66 y + 132 + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

$- 66 y + 132 + 14 y - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Simplify by adding terms.

Add $- 66 y$ and $14 y$ .

$- 52 y + 132 - 18 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Subtract $18$ from $132$ .

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 - 2 x - 4 y$

Replace all occurrences of $x$ in $z = 6 - 2 x - 4 y$ with $- \frac{22 y}{3} + \frac{44}{3}$ .

$z = 6 - 2 (- \frac{22 y}{3} + \frac{44}{3}) - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Simplify the right side.

Simplify $6 - 2 (- \frac{22 y}{3} + \frac{44}{3}) - 4 y$ .

Simplify each term.

Apply the distributive property.

$z = 6 - 2 (- \frac{22 y}{3}) - 2 (\frac{44}{3}) - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Multiply $- 2 (- \frac{22 y}{3})$ .

Multiply $- 1$ by $- 2$ .

$z = 6 + 2 (\frac{22 y}{3}) - 2 (\frac{44}{3}) - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Combine $2$ and $\frac{22 y}{3}$ .

$z = 6 + \frac{2 (22 y)}{3} - 2 (\frac{44}{3}) - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Multiply $22$ by $2$ .

$z = 6 + \frac{44 y}{3} - 2 (\frac{44}{3}) - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 + \frac{44 y}{3} - 2 (\frac{44}{3}) - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Multiply $- 2 (\frac{44}{3})$ .

Combine $- 2$ and $\frac{44}{3}$ .

$z = 6 + \frac{44 y}{3} + \frac{- 2 \cdot 44}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Multiply $- 2$ by $44$ .

$z = 6 + \frac{44 y}{3} + \frac{- 88}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 + \frac{44 y}{3} + \frac{- 88}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Move the negative in front of the fraction.

$z = 6 + \frac{44 y}{3} - \frac{88}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = 6 + \frac{44 y}{3} - \frac{88}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$z = \frac{44 y}{3} + 6 \cdot \frac{3}{3} - \frac{88}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Combine $6$ and $\frac{3}{3}$ .

$z = \frac{44 y}{3} + \frac{6 \cdot 3}{3} - \frac{88}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Combine the numerators over the common denominator.

$z = \frac{44 y}{3} + \frac{6 \cdot 3 - 88}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Simplify the numerator.

Multiply $6$ by $3$ .

$z = \frac{44 y}{3} + \frac{18 - 88}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Subtract $88$ from $18$ .

$z = \frac{44 y}{3} + \frac{- 70}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{44 y}{3} + \frac{- 70}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Move the negative in front of the fraction.

$z = \frac{44 y}{3} - \frac{70}{3} - 4 y$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

To write $- 4 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$z = \frac{44 y}{3} - 4 y \cdot \frac{3}{3} - \frac{70}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Combine $- 4 y$ and $\frac{3}{3}$ .

$z = \frac{44 y}{3} + \frac{- 4 y \cdot 3}{3} - \frac{70}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Combine the numerators over the common denominator.

$z = \frac{44 y - 4 y \cdot 3}{3} - \frac{70}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Combine the numerators over the common denominator.

$z = \frac{44 y - 4 y \cdot 3 - 70}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Multiply $3$ by $- 4$ .

$z = \frac{44 y - 12 y - 70}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Subtract $12 y$ from $44 y$ .

$z = \frac{32 y - 70}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Factor $2$ out of $32 y - 70$ .

Factor $2$ out of $32 y$ .

$z = \frac{2 (16 y) - 70}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Factor $2$ out of $- 70$ .

$z = \frac{2 (16 y) + 2 (- 35)}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Factor $2$ out of $2 (16 y) + 2 (- 35)$ .

$z = \frac{2 (16 y - 35)}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{2 (16 y - 35)}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{2 (16 y - 35)}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{2 (16 y - 35)}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{2 (16 y - 35)}{3}$

$- 52 y + 114 = - 2$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Solve for $y$ in $- 52 y + 114 = - 2$ .

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

Subtract $114$ from both sides of the equation.

$- 52 y = - 2 - 114$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Subtract $114$ from $- 2$ .

$- 52 y = - 116$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$- 52 y = - 116$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Divide each term in $- 52 y = - 116$ by $- 52$ and simplify.

Divide each term in $- 52 y = - 116$ by $- 52$ .

$\frac{- 52 y}{- 52} = \frac{- 116}{- 52}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Simplify the left side.

Cancel the common factor of $- 52$ .

Cancel the common factor.

$\frac{- 52 y}{- 52} = \frac{- 116}{- 52}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Divide $y$ by $1$ .

$y = \frac{- 116}{- 52}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$y = \frac{- 116}{- 52}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$y = \frac{- 116}{- 52}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Simplify the right side.

Cancel the common factor of $- 116$ and $- 52$ .

Factor $- 4$ out of $- 116$ .

$y = \frac{- 4 \cdot 29}{- 52}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Cancel the common factors.

Factor $- 4$ out of $- 52$ .

$y = \frac{- 4 \cdot 29}{- 4 \cdot 13}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Cancel the common factor.

$y = \frac{- 4 \cdot 29}{- 4 \cdot 13}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Rewrite the expression.

$y = \frac{29}{13}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$y = \frac{29}{13}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$y = \frac{29}{13}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$y = \frac{29}{13}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$y = \frac{29}{13}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$y = \frac{29}{13}$

$z = \frac{2 (16 y - 35)}{3}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Replace all occurrences of $y$ with $\frac{29}{13}$ in each equation.

Replace all occurrences of $y$ in $z = \frac{2 (16 y - 35)}{3}$ with $\frac{29}{13}$ .

$z = \frac{2 (16 (\frac{29}{13}) - 35)}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Simplify the right side.

Simplify $\frac{2 (16 (\frac{29}{13}) - 35)}{3}$ .

Simplify the numerator.

Multiply $16 (\frac{29}{13})$ .

Combine $16$ and $\frac{29}{13}$ .

$z = \frac{2 (\frac{16 \cdot 29}{13} - 35)}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Multiply $16$ by $29$ .

$z = \frac{2 (\frac{464}{13} - 35)}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{2 (\frac{464}{13} - 35)}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

To write $- 35$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$z = \frac{2 (\frac{464}{13} - 35 \cdot \frac{13}{13})}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Combine $- 35$ and $\frac{13}{13}$ .

$z = \frac{2 (\frac{464}{13} + \frac{- 35 \cdot 13}{13})}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Combine the numerators over the common denominator.

$z = \frac{2 (\frac{464 - 35 \cdot 13}{13})}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Simplify the numerator.

Multiply $- 35$ by $13$ .

$z = \frac{2 (\frac{464 - 455}{13})}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Subtract $455$ from $464$ .

$z = \frac{2 (\frac{9}{13})}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{2 (\frac{9}{13})}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{2 (\frac{9}{13})}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Combine fractions.

Combine $2$ and $\frac{9}{13}$ .

$z = \frac{\frac{2 \cdot 9}{13}}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Multiply $2$ by $9$ .

$z = \frac{\frac{18}{13}}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{\frac{18}{13}}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Multiply the numerator by the reciprocal of the denominator.

$z = \frac{18}{13} \cdot \frac{1}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $18$ .

$z = \frac{3 (6)}{13} \cdot \frac{1}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Cancel the common factor.

$z = \frac{3 \cdot 6}{13} \cdot \frac{1}{3}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Rewrite the expression.

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = - \frac{22 y}{3} + \frac{44}{3}$

Replace all occurrences of $y$ in $x = - \frac{22 y}{3} + \frac{44}{3}$ with $\frac{29}{13}$ .

$x = - \frac{22 (\frac{29}{13})}{3} + \frac{44}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Simplify the right side.

Simplify $- \frac{22 (\frac{29}{13})}{3} + \frac{44}{3}$ .

Combine the numerators over the common denominator.

$x = \frac{- 22 (\frac{29}{13}) + 44}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Simplify each term.

Multiply $- 22 (\frac{29}{13})$ .

Combine $- 22$ and $\frac{29}{13}$ .

$x = \frac{\frac{- 22 \cdot 29}{13} + 44}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Multiply $- 22$ by $29$ .

$x = \frac{\frac{- 638}{13} + 44}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = \frac{\frac{- 638}{13} + 44}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Move the negative in front of the fraction.

$x = \frac{- \frac{638}{13} + 44}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = \frac{- \frac{638}{13} + 44}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

To write $44$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$x = \frac{- \frac{638}{13} + 44 \cdot \frac{13}{13}}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Combine $44$ and $\frac{13}{13}$ .

$x = \frac{- \frac{638}{13} + \frac{44 \cdot 13}{13}}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Combine the numerators over the common denominator.

$x = \frac{\frac{- 638 + 44 \cdot 13}{13}}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Simplify the numerator.

Multiply $44$ by $13$ .

$x = \frac{\frac{- 638 + 572}{13}}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Add $- 638$ and $572$ .

$x = \frac{\frac{- 66}{13}}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = \frac{\frac{- 66}{13}}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Move the negative in front of the fraction.

$x = \frac{- \frac{66}{13}}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{66}{13} \cdot \frac{1}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{66}{13}$ into the numerator.

$x = \frac{- 66}{13} \cdot \frac{1}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Factor $3$ out of $- 66$ .

$x = \frac{3 (- 22)}{13} \cdot \frac{1}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Cancel the common factor.

$x = \frac{3 \cdot - 22}{13} \cdot \frac{1}{3}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Rewrite the expression.

$x = \frac{- 22}{13}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = \frac{- 22}{13}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

Move the negative in front of the fraction.

$x = - \frac{22}{13}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = - \frac{22}{13}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = - \frac{22}{13}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

$x = - \frac{22}{13}$

$z = \frac{6}{13}$

$y = \frac{29}{13}$

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

$(- \frac{22}{13}, \frac{29}{13}, \frac{6}{13})$

The result can be shown in multiple forms.

Point Form:

$(- \frac{22}{13}, \frac{29}{13}, \frac{6}{13})$

Equation Form:

$x = - \frac{22}{13}, y = \frac{29}{13}, z = \frac{6}{13}$

Solve the System of Equations 3x+2y-3z=-2 7x-2y+5z=-14 2x+4y+z=6

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