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

$- 5 x - 3 y + z = - 4$ $- 2 x - 2 y + 2 z = 4$ $z = x + 5$

Step 1

Replace all occurrences of $z$ with $x + 5$ in each equation.

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

$- 5 x - 3 y + x + 5 = - 4$

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

$z = x + 5$

Simplify the left side.

Simplify $- 5 x - 3 y + x + 5$ .

Remove parentheses.

$- 5 x - 3 y + x + 5 = - 4$

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

$z = x + 5$

Add $- 5 x$ and $x$ .

$- 4 x - 3 y + 5 = - 4$

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

$z = x + 5$

$- 4 x - 3 y + 5 = - 4$

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

$z = x + 5$

$- 4 x - 3 y + 5 = - 4$

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

$z = x + 5$

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

$- 2 x - 2 y + 2 (x + 5) = 4$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Simplify the left side.

Simplify $- 2 x - 2 y + 2 (x + 5)$ .

Simplify each term.

Apply the distributive property.

$- 2 x - 2 y + 2 x + 2 \cdot 5 = 4$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Multiply $2$ by $5$ .

$- 2 x - 2 y + 2 x + 10 = 4$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$- 2 x - 2 y + 2 x + 10 = 4$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Combine the opposite terms in $- 2 x - 2 y + 2 x + 10$ .

Add $- 2 x$ and $2 x$ .

$- 2 y + 0 + 10 = 4$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Add $- 2 y$ and $0$ .

$- 2 y + 10 = 4$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$- 2 y + 10 = 4$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$- 2 y + 10 = 4$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$- 2 y + 10 = 4$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$- 2 y + 10 = 4$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Step 2

Solve for $y$ in $- 2 y + 10 = 4$ .

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

Subtract $10$ from both sides of the equation.

$- 2 y = 4 - 10$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Subtract $10$ from $4$ .

$- 2 y = - 6$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$- 2 y = - 6$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Divide each term in $- 2 y = - 6$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 6$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 6}{- 2}$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 6}{- 2}$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 2}$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$y = \frac{- 6}{- 2}$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$y = \frac{- 6}{- 2}$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Simplify the right side.

Divide $- 6$ by $- 2$ .

$y = 3$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$y = 3$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$y = 3$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

$y = 3$

$- 4 x - 3 y + 5 = - 4$

$z = x + 5$

Step 3

Replace all occurrences of $y$ with $3$ in each equation.

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

$- 4 x - 3 \cdot 3 + 5 = - 4$

$y = 3$

$z = x + 5$

Simplify the left side.

Simplify $- 4 x - 3 \cdot 3 + 5$ .

Multiply $- 3$ by $3$ .

$- 4 x - 9 + 5 = - 4$

$y = 3$

$z = x + 5$

Add $- 9$ and $5$ .

$- 4 x - 4 = - 4$

$y = 3$

$z = x + 5$

$- 4 x - 4 = - 4$

$y = 3$

$z = x + 5$

$- 4 x - 4 = - 4$

$y = 3$

$z = x + 5$

$- 4 x - 4 = - 4$

$y = 3$

$z = x + 5$

Step 4

Solve for $x$ in $- 4 x - 4 = - 4$ .

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

Add $4$ to both sides of the equation.

$- 4 x = - 4 + 4$

$y = 3$

$z = x + 5$

Add $- 4$ and $4$ .

$- 4 x = 0$

$y = 3$

$z = x + 5$

$- 4 x = 0$

$y = 3$

$z = x + 5$

Divide each term in $- 4 x = 0$ by $- 4$ and simplify.

Divide each term in $- 4 x = 0$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{0}{- 4}$

$y = 3$

$z = x + 5$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{0}{- 4}$

$y = 3$

$z = x + 5$

Divide $x$ by $1$ .

$x = \frac{0}{- 4}$

$y = 3$

$z = x + 5$

$x = \frac{0}{- 4}$

$y = 3$

$z = x + 5$

$x = \frac{0}{- 4}$

$y = 3$

$z = x + 5$

Simplify the right side.

Divide $0$ by $- 4$ .

$x = 0$

$y = 3$

$z = x + 5$

$x = 0$

$y = 3$

$z = x + 5$

$x = 0$

$y = 3$

$z = x + 5$

$x = 0$

$y = 3$

$z = x + 5$

Step 5

Replace all occurrences of $x$ with $0$ in each equation.

Replace all occurrences of $x$ in $z = x + 5$ with $0$ .

$z = (0) + 5$

$x = 0$

$y = 3$

Simplify the right side.

Add $0$ and $5$ .

$z = 5$

$x = 0$

$y = 3$

$z = 5$

$x = 0$

$y = 3$

$z = 5$

$x = 0$

$y = 3$

Step 6

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

$(0, 3, 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(0, 3, 5)$

Equation Form:

$x = 0, y = 3, z = 5$

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

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