Solve by Substitution 2x-2y=-8 , x+2y=-1

$2 x - 2 y = - 8$ , $x + 2 y = - 1$

Step 1

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

$x = - 1 - 2 y$

$2 x - 2 y = - 8$

Step 2

Replace all occurrences of $x$ with $- 1 - 2 y$ in each equation.

Replace all occurrences of $x$ in $2 x - 2 y = - 8$ with $- 1 - 2 y$ .

$2 (- 1 - 2 y) - 2 y = - 8$

$x = - 1 - 2 y$

Simplify the left side.

Simplify $2 (- 1 - 2 y) - 2 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot - 1 + 2 (- 2 y) - 2 y = - 8$

$x = - 1 - 2 y$

Multiply $2$ by $- 1$ .

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

$x = - 1 - 2 y$

Multiply $- 2$ by $2$ .

$- 2 - 4 y - 2 y = - 8$

$x = - 1 - 2 y$

$- 2 - 4 y - 2 y = - 8$

$x = - 1 - 2 y$

Subtract $2 y$ from $- 4 y$ .

$- 2 - 6 y = - 8$

$x = - 1 - 2 y$

$- 2 - 6 y = - 8$

$x = - 1 - 2 y$

$- 2 - 6 y = - 8$

$x = - 1 - 2 y$

$- 2 - 6 y = - 8$

$x = - 1 - 2 y$

Step 3

Solve for $y$ in $- 2 - 6 y = - 8$ .

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

Add $2$ to both sides of the equation.

$- 6 y = - 8 + 2$

$x = - 1 - 2 y$

Add $- 8$ and $2$ .

$- 6 y = - 6$

$x = - 1 - 2 y$

$- 6 y = - 6$

$x = - 1 - 2 y$

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

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

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

$x = - 1 - 2 y$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

$x = - 1 - 2 y$

Divide $y$ by $1$ .

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

$x = - 1 - 2 y$

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

$x = - 1 - 2 y$

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

$x = - 1 - 2 y$

Simplify the right side.

Divide $- 6$ by $- 6$ .

$y = 1$

$x = - 1 - 2 y$

$y = 1$

$x = - 1 - 2 y$

$y = 1$

$x = - 1 - 2 y$

$y = 1$

$x = - 1 - 2 y$

Step 4

Replace all occurrences of $y$ with $1$ in each equation.

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

$x = - 1 - 2 \cdot 1$

$y = 1$

Simplify the right side.

Simplify $- 1 - 2 \cdot 1$ .

Multiply $- 2$ by $1$ .

$x = - 1 - 2$

$y = 1$

Subtract $2$ from $- 1$ .

$x = - 3$

$y = 1$

$x = - 3$

$y = 1$

$x = - 3$

$y = 1$

$x = - 3$

$y = 1$

Step 5

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

$(- 3, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 3, 1)$

Equation Form:

$x = - 3, y = 1$

Step 7

Solve by Substitution 2x-2y=-8 , x+2y=-1

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