Solve by Substitution -x-y-z=-8 , -4x+4y+5z=7 , 2x+2z=4

$- x - y - z = - 8$ , $- 4 x + 4 y + 5 z = 7$ , $2 x + 2 z = 4$

Step 1

Solve for $x$ in $- x - y - z = - 8$ .

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

Add $y$ to both sides of the equation.

$- x - z = - 8 + y$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

Add $z$ to both sides of the equation.

$- x = - 8 + y + z$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

$- x = - 8 + y + z$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

Divide each term in $- x = - 8 + y + z$ by $- 1$ and simplify.

Divide each term in $- x = - 8 + y + z$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 8}{- 1} + \frac{y}{- 1} + \frac{z}{- 1}$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 8}{- 1} + \frac{y}{- 1} + \frac{z}{- 1}$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 1} + \frac{y}{- 1} + \frac{z}{- 1}$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

$x = \frac{- 8}{- 1} + \frac{y}{- 1} + \frac{z}{- 1}$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

Simplify the right side.

Simplify each term.

Divide $- 8$ by $- 1$ .

$x = 8 + \frac{y}{- 1} + \frac{z}{- 1}$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

Move the negative one from the denominator of $\frac{y}{- 1}$ .

$x = 8 - 1 \cdot y + \frac{z}{- 1}$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

Rewrite $- 1 \cdot y$ as $- y$ .

$x = 8 - y + \frac{z}{- 1}$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

Move the negative one from the denominator of $\frac{z}{- 1}$ .

$x = 8 - y - 1 \cdot z$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

Rewrite $- 1 \cdot z$ as $- z$ .

$x = 8 - y - z$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

$x = 8 - y - z$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

$x = 8 - y - z$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

$x = 8 - y - z$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

$x = 8 - y - z$

$- 4 x + 4 y + 5 z = 7$

$2 x + 2 z = 4$

Step 2

Replace all occurrences of $x$ with $8 - y - z$ in each equation.

Replace all occurrences of $x$ in $- 4 x + 4 y + 5 z = 7$ with $8 - y - z$ .

$- 4 (8 - y - z) + 4 y + 5 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

Simplify the left side.

Simplify $- 4 (8 - y - z) + 4 y + 5 z$ .

Simplify each term.

Apply the distributive property.

$- 4 \cdot 8 - 4 (- y) - 4 (- z) + 4 y + 5 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

Simplify.

Multiply $- 4$ by $8$ .

$- 32 - 4 (- y) - 4 (- z) + 4 y + 5 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

Multiply $- 1$ by $- 4$ .

$- 32 + 4 y - 4 (- z) + 4 y + 5 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

Multiply $- 1$ by $- 4$ .

$- 32 + 4 y + 4 z + 4 y + 5 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

$- 32 + 4 y + 4 z + 4 y + 5 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

$- 32 + 4 y + 4 z + 4 y + 5 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

Simplify by adding terms.

Add $4 y$ and $4 y$ .

$- 32 + 8 y + 4 z + 5 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

Add $4 z$ and $5 z$ .

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$2 x + 2 z = 4$

Replace all occurrences of $x$ in $2 x + 2 z = 4$ with $8 - y - z$ .

$2 (8 - y - z) + 2 z = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Simplify the left side.

Simplify $2 (8 - y - z) + 2 z$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 8 + 2 (- y) + 2 (- z) + 2 z = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Simplify.

Multiply $2$ by $8$ .

$16 + 2 (- y) + 2 (- z) + 2 z = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Multiply $- 1$ by $2$ .

$16 - 2 y + 2 (- z) + 2 z = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Multiply $- 1$ by $2$ .

$16 - 2 y - 2 z + 2 z = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$16 - 2 y - 2 z + 2 z = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$16 - 2 y - 2 z + 2 z = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Combine the opposite terms in $16 - 2 y - 2 z + 2 z$ .

Add $- 2 z$ and $2 z$ .

$16 - 2 y + 0 = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Add $16 - 2 y$ and $0$ .

$16 - 2 y = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$16 - 2 y = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$16 - 2 y = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$16 - 2 y = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$16 - 2 y = 4$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Step 3

Solve for $y$ in $16 - 2 y = 4$ .

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

Subtract $16$ from both sides of the equation.

$- 2 y = 4 - 16$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Subtract $16$ from $4$ .

$- 2 y = - 12$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$- 2 y = - 12$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Divide each term in $- 2 y = - 12$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 12$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 12}{- 2}$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 12}{- 2}$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Divide $y$ by $1$ .

$y = \frac{- 12}{- 2}$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$y = \frac{- 12}{- 2}$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$y = \frac{- 12}{- 2}$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$y = 6$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$y = 6$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$y = 6$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

$y = 6$

$- 32 + 8 y + 9 z = 7$

$x = 8 - y - z$

Step 4

Replace all occurrences of $y$ with $6$ in each equation.

Replace all occurrences of $y$ in $- 32 + 8 y + 9 z = 7$ with $6$ .

$- 32 + 8 (6) + 9 z = 7$

$y = 6$

$x = 8 - y - z$

Simplify the left side.

Simplify $- 32 + 8 (6) + 9 z$ .

Multiply $8$ by $6$ .

$- 32 + 48 + 9 z = 7$

$y = 6$

$x = 8 - y - z$

Add $- 32$ and $48$ .

$16 + 9 z = 7$

$y = 6$

$x = 8 - y - z$

$16 + 9 z = 7$

$y = 6$

$x = 8 - y - z$

$16 + 9 z = 7$

$y = 6$

$x = 8 - y - z$

Replace all occurrences of $y$ in $x = 8 - y - z$ with $6$ .

$x = 8 - (6) - z$

$16 + 9 z = 7$

$y = 6$

Simplify the right side.

Simplify $8 - (6) - z$ .

Multiply $- 1$ by $6$ .

$x = 8 - 6 - z$

$16 + 9 z = 7$

$y = 6$

Subtract $6$ from $8$ .

$x = 2 - z$

$16 + 9 z = 7$

$y = 6$

$x = 2 - z$

$16 + 9 z = 7$

$y = 6$

$x = 2 - z$

$16 + 9 z = 7$

$y = 6$

$x = 2 - z$

$16 + 9 z = 7$

$y = 6$

Step 5

Solve for $z$ in $16 + 9 z = 7$ .

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

Subtract $16$ from both sides of the equation.

$9 z = 7 - 16$

$x = 2 - z$

$y = 6$

Subtract $16$ from $7$ .

$9 z = - 9$

$x = 2 - z$

$y = 6$

$9 z = - 9$

$x = 2 - z$

$y = 6$

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

Divide each term in $9 z = - 9$ by $9$ .

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

$x = 2 - z$

$y = 6$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

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

$x = 2 - z$

$y = 6$

Divide $z$ by $1$ .

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

$x = 2 - z$

$y = 6$

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

$x = 2 - z$

$y = 6$

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

$x = 2 - z$

$y = 6$

Simplify the right side.

Divide $- 9$ by $9$ .

$z = - 1$

$x = 2 - z$

$y = 6$

$z = - 1$

$x = 2 - z$

$y = 6$

$z = - 1$

$x = 2 - z$

$y = 6$

$z = - 1$

$x = 2 - z$

$y = 6$

Step 6

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

Replace all occurrences of $z$ in $x = 2 - z$ with $- 1$ .

$x = 2 - (- 1)$

$z = - 1$

$y = 6$

Simplify the right side.

Simplify $2 - (- 1)$ .

Multiply $- 1$ by $- 1$ .

$x = 2 + 1$

$z = - 1$

$y = 6$

Add $2$ and $1$ .

$x = 3$

$z = - 1$

$y = 6$

$x = 3$

$z = - 1$

$y = 6$

$x = 3$

$z = - 1$

$y = 6$

$x = 3$

$z = - 1$

$y = 6$

Step 7

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

$(3, 6, - 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(3, 6, - 1)$

Equation Form:

$x = 3, y = 6, z = - 1$

Solve by Substitution -x-y-z=-8 , -4x+4y+5z=7 , 2x+2z=4

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