Solve the System of Equations x+y-2z=7 7x+9y-2z=-9 10x+7y+2z=-3

$x + y - 2 z = 7$ $7 x + 9 y - 2 z = - 9$ $10 x + 7 y + 2 z = - 3$

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

Subtract $y$ from both sides of the equation.

$x - 2 z = 7 - y$

$7 x + 9 y - 2 z = - 9$

$10 x + 7 y + 2 z = - 3$

Add $2 z$ to both sides of the equation.

$x = 7 - y + 2 z$

$7 x + 9 y - 2 z = - 9$

$10 x + 7 y + 2 z = - 3$

$x = 7 - y + 2 z$

$7 x + 9 y - 2 z = - 9$

$10 x + 7 y + 2 z = - 3$

Replace all occurrences of $x$ with $7 - y + 2 z$ in each equation.

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

$7 (7 - y + 2 z) + 9 y - 2 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

Simplify the left side.

Simplify $7 (7 - y + 2 z) + 9 y - 2 z$ .

Simplify each term.

Apply the distributive property.

$7 \cdot 7 + 7 (- y) + 7 (2 z) + 9 y - 2 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

Simplify.

Multiply $7$ by $7$ .

$49 + 7 (- y) + 7 (2 z) + 9 y - 2 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

Multiply $- 1$ by $7$ .

$49 - 7 y + 7 (2 z) + 9 y - 2 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

Multiply $2$ by $7$ .

$49 - 7 y + 14 z + 9 y - 2 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

$49 - 7 y + 14 z + 9 y - 2 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

$49 - 7 y + 14 z + 9 y - 2 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

Simplify by adding terms.

Add $- 7 y$ and $9 y$ .

$49 + 2 y + 14 z - 2 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

Subtract $2 z$ from $14 z$ .

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$10 x + 7 y + 2 z = - 3$

Replace all occurrences of $x$ in $10 x + 7 y + 2 z = - 3$ with $7 - y + 2 z$ .

$10 (7 - y + 2 z) + 7 y + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Simplify the left side.

Simplify $10 (7 - y + 2 z) + 7 y + 2 z$ .

Simplify each term.

Apply the distributive property.

$10 \cdot 7 + 10 (- y) + 10 (2 z) + 7 y + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Simplify.

Multiply $10$ by $7$ .

$70 + 10 (- y) + 10 (2 z) + 7 y + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Multiply $- 1$ by $10$ .

$70 - 10 y + 10 (2 z) + 7 y + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Multiply $2$ by $10$ .

$70 - 10 y + 20 z + 7 y + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$70 - 10 y + 20 z + 7 y + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$70 - 10 y + 20 z + 7 y + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Simplify by adding terms.

Add $- 10 y$ and $7 y$ .

$70 - 3 y + 20 z + 2 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Add $20 z$ and $2 z$ .

$70 - 3 y + 22 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$70 - 3 y + 22 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$70 - 3 y + 22 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$70 - 3 y + 22 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$70 - 3 y + 22 z = - 3$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Solve for $y$ in $70 - 3 y + 22 z = - 3$ .

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

Subtract $70$ from both sides of the equation.

$- 3 y + 22 z = - 3 - 70$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Subtract $22 z$ from both sides of the equation.

$- 3 y = - 3 - 70 - 22 z$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Subtract $70$ from $- 3$ .

$- 3 y = - 73 - 22 z$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$- 3 y = - 73 - 22 z$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Divide each term in $- 3 y = - 73 - 22 z$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 73 - 22 z$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 73}{- 3} + \frac{- 22 z}{- 3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 73}{- 3} + \frac{- 22 z}{- 3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Divide $y$ by $1$ .

$y = \frac{- 73}{- 3} + \frac{- 22 z}{- 3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$y = \frac{- 73}{- 3} + \frac{- 22 z}{- 3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$y = \frac{- 73}{- 3} + \frac{- 22 z}{- 3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{73}{3} + \frac{- 22 z}{- 3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Dividing two negative values results in a positive value.

$y = \frac{73}{3} + \frac{22 z}{3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$y = \frac{73}{3} + \frac{22 z}{3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$y = \frac{73}{3} + \frac{22 z}{3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$y = \frac{73}{3} + \frac{22 z}{3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

$y = \frac{73}{3} + \frac{22 z}{3}$

$49 + 2 y + 12 z = - 9$

$x = 7 - y + 2 z$

Replace all occurrences of $y$ with $\frac{73}{3} + \frac{22 z}{3}$ in each equation.

Replace all occurrences of $y$ in $49 + 2 y + 12 z = - 9$ with $\frac{73}{3} + \frac{22 z}{3}$ .

$49 + 2 (\frac{73}{3} + \frac{22 z}{3}) + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Simplify the left side.

Simplify $49 + 2 (\frac{73}{3} + \frac{22 z}{3}) + 12 z$ .

Simplify each term.

Apply the distributive property.

$49 + 2 (\frac{73}{3}) + 2 (\frac{22 z}{3}) + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Multiply $2 (\frac{73}{3})$ .

Combine $2$ and $\frac{73}{3}$ .

$49 + \frac{2 \cdot 73}{3} + 2 (\frac{22 z}{3}) + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Multiply $2$ by $73$ .

$49 + \frac{146}{3} + 2 (\frac{22 z}{3}) + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

$49 + \frac{146}{3} + 2 (\frac{22 z}{3}) + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Multiply $2 \frac{22 z}{3}$ .

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

$49 + \frac{146}{3} + \frac{2 (22 z)}{3} + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Multiply $22$ by $2$ .

$49 + \frac{146}{3} + \frac{44 z}{3} + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

$49 + \frac{146}{3} + \frac{44 z}{3} + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

$49 + \frac{146}{3} + \frac{44 z}{3} + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

To write $49$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$49 \cdot \frac{3}{3} + \frac{146}{3} + \frac{44 z}{3} + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Combine $49$ and $\frac{3}{3}$ .

$\frac{49 \cdot 3}{3} + \frac{146}{3} + \frac{44 z}{3} + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Combine the numerators over the common denominator.

$\frac{49 \cdot 3 + 146}{3} + \frac{44 z}{3} + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Simplify the numerator.

Multiply $49$ by $3$ .

$\frac{147 + 146}{3} + \frac{44 z}{3} + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Add $147$ and $146$ .

$\frac{293}{3} + \frac{44 z}{3} + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

$\frac{293}{3} + \frac{44 z}{3} + 12 z = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

To write $12 z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{293}{3} + \frac{44 z}{3} + 12 z \cdot \frac{3}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Combine $12 z$ and $\frac{3}{3}$ .

$\frac{293}{3} + \frac{44 z}{3} + \frac{12 z \cdot 3}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Combine the numerators over the common denominator.

$\frac{293}{3} + \frac{44 z + 12 z \cdot 3}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Combine the numerators over the common denominator.

$\frac{293 + 44 z + 12 z \cdot 3}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Multiply $3$ by $12$ .

$\frac{293 + 44 z + 36 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Add $44 z$ and $36 z$ .

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 7 - y + 2 z$

Replace all occurrences of $y$ in $x = 7 - y + 2 z$ with $\frac{73}{3} + \frac{22 z}{3}$ .

$x = 7 - (\frac{73}{3} + \frac{22 z}{3}) + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Simplify the right side.

Simplify $7 - (\frac{73}{3} + \frac{22 z}{3}) + 2 z$ .

Apply the distributive property.

$x = 7 - \frac{73}{3} - \frac{22 z}{3} + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

To write $7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = 7 \cdot \frac{3}{3} - \frac{73}{3} - \frac{22 z}{3} + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Combine $7$ and $\frac{3}{3}$ .

$x = \frac{7 \cdot 3}{3} - \frac{73}{3} - \frac{22 z}{3} + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Combine the numerators over the common denominator.

$x = \frac{7 \cdot 3 - 73}{3} - \frac{22 z}{3} + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Simplify the numerator.

Multiply $7$ by $3$ .

$x = \frac{21 - 73}{3} - \frac{22 z}{3} + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Subtract $73$ from $21$ .

$x = \frac{- 52}{3} - \frac{22 z}{3} + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = \frac{- 52}{3} - \frac{22 z}{3} + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Move the negative in front of the fraction.

$x = - \frac{52}{3} - \frac{22 z}{3} + 2 z$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

To write $2 z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = - \frac{52}{3} - \frac{22 z}{3} + 2 z \cdot \frac{3}{3}$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

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

$x = - \frac{52}{3} - \frac{22 z}{3} + \frac{2 z \cdot 3}{3}$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Combine the numerators over the common denominator.

$x = - \frac{52}{3} + \frac{- 22 z + 2 z \cdot 3}{3}$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Combine the numerators over the common denominator.

$x = \frac{- 52 - 22 z + 2 z \cdot 3}{3}$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Multiply $3$ by $2$ .

$x = \frac{- 52 - 22 z + 6 z}{3}$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Add $- 22 z$ and $6 z$ .

$x = \frac{- 52 - 16 z}{3}$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Factor $4$ out of $- 52 - 16 z$ .

Factor $4$ out of $- 52$ .

$x = \frac{4 (- 13) - 16 z}{3}$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Factor $4$ out of $- 16 z$ .

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

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Factor $4$ out of $4 (- 13) + 4 (- 4 z)$ .

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

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

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

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

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

$x = \frac{4 (- 1 \cdot 13 - 4 z)}{3}$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Factor $- 1$ out of $- 4 z$ .

$x = \frac{4 (- 1 \cdot 13 - (4 z))}{3}$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Factor $- 1$ out of $- 1 (13) - (4 z)$ .

$x = \frac{4 (- 1 (13 + 4 z))}{3}$

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Move the negative in front of the fraction.

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

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

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

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

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

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

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

$\frac{293 + 80 z}{3} = - 9$

$y = \frac{73}{3} + \frac{22 z}{3}$

Solve for $z$ in $\frac{293 + 80 z}{3} = - 9$ .

Multiply both sides by $3$ .

$\frac{293 + 80 z}{3} \cdot 3 = - 9 \cdot 3$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

Simplify.

Simplify the left side.

Simplify $\frac{293 + 80 z}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{293 + 80 z}{3} \cdot 3 = - 9 \cdot 3$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

Rewrite the expression.

$293 + 80 z = - 9 \cdot 3$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$293 + 80 z = - 9 \cdot 3$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

Reorder $293$ and $80 z$ .

$80 z + 293 = - 9 \cdot 3$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$80 z + 293 = - 9 \cdot 3$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$80 z + 293 = - 9 \cdot 3$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

Simplify the right side.

Multiply $- 9$ by $3$ .

$80 z + 293 = - 27$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$80 z + 293 = - 27$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$80 z + 293 = - 27$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

Solve for $z$ .

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

Subtract $293$ from both sides of the equation.

$80 z = - 27 - 293$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

Subtract $293$ from $- 27$ .

$80 z = - 320$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$80 z = - 320$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

Divide each term in $80 z = - 320$ by $80$ and simplify.

Divide each term in $80 z = - 320$ by $80$ .

$\frac{80 z}{80} = \frac{- 320}{80}$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

Simplify the left side.

Cancel the common factor of $80$ .

Cancel the common factor.

$\frac{80 z}{80} = \frac{- 320}{80}$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

Divide $z$ by $1$ .

$z = \frac{- 320}{80}$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$z = \frac{- 320}{80}$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$z = \frac{- 320}{80}$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

Simplify the right side.

Divide $- 320$ by $80$ .

$z = - 4$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$z = - 4$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$z = - 4$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$z = - 4$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

$z = - 4$

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

$y = \frac{73}{3} + \frac{22 z}{3}$

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

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

$x = - \frac{4 (13 + 4 (- 4))}{3}$

$z = - 4$

$y = \frac{73}{3} + \frac{22 z}{3}$

Simplify the right side.

Simplify $- \frac{4 (13 + 4 (- 4))}{3}$ .

Simplify the numerator.

Multiply $4$ by $- 4$ .

$x = - \frac{4 (13 - 16)}{3}$

$z = - 4$

$y = \frac{73}{3} + \frac{22 z}{3}$

Subtract $16$ from $13$ .

$x = - \frac{4 \cdot - 3}{3}$

$z = - 4$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = - \frac{4 \cdot - 3}{3}$

$z = - 4$

$y = \frac{73}{3} + \frac{22 z}{3}$

Simplify the expression.

Multiply $4$ by $- 3$ .

$x = - \frac{- 12}{3}$

$z = - 4$

$y = \frac{73}{3} + \frac{22 z}{3}$

Divide $- 12$ by $3$ .

$x = 4$

$z = - 4$

$y = \frac{73}{3} + \frac{22 z}{3}$

Multiply $- 1$ by $- 4$ .

$x = 4$

$z = - 4$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 4$

$z = - 4$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 4$

$z = - 4$

$y = \frac{73}{3} + \frac{22 z}{3}$

$x = 4$

$z = - 4$

$y = \frac{73}{3} + \frac{22 z}{3}$

Replace all occurrences of $z$ in $y = \frac{73}{3} + \frac{22 z}{3}$ with $- 4$ .

$y = \frac{73}{3} + \frac{22 (- 4)}{3}$

$x = 4$

$z = - 4$

Simplify the right side.

Simplify $\frac{73}{3} + \frac{22 (- 4)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{73 + 22 (- 4)}{3}$

$x = 4$

$z = - 4$

Simplify the expression.

Multiply $22$ by $- 4$ .

$y = \frac{73 - 88}{3}$

$x = 4$

$z = - 4$

Subtract $88$ from $73$ .

$y = \frac{- 15}{3}$

$x = 4$

$z = - 4$

Divide $- 15$ by $3$ .

$y = - 5$

$x = 4$

$z = - 4$

$y = - 5$

$x = 4$

$z = - 4$

$y = - 5$

$x = 4$

$z = - 4$

$y = - 5$

$x = 4$

$z = - 4$

$y = - 5$

$x = 4$

$z = - 4$

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

$(4, - 5, - 4)$

The result can be shown in multiple forms.

Point Form:

$(4, - 5, - 4)$

Equation Form:

$x = 4, y = - 5, z = - 4$

Solve the System of Equations x+y-2z=7 7x+9y-2z=-9 10x+7y+2z=-3

Related Questions

Support LCMGCF.com by disabling your adblocker.