Solve the System of Equations x+2y=-8 y=-3/2x-6

$x + 2 y = - 8$ $y = - \frac{3}{2} x - 6$

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

$x = - 8 - 2 y$

$y = - \frac{3}{2} x - 6$

Replace all occurrences of $x$ with $- 8 - 2 y$ in each equation.

Replace all occurrences of $x$ in $y = - \frac{3}{2} x - 6$ with $- 8 - 2 y$ .

$y = - \frac{3}{2} \cdot (- 8 - 2 y) - 6$

$x = - 8 - 2 y$

Simplify the right side.

Simplify $- \frac{3}{2} \cdot (- 8 - 2 y) - 6$ .

Simplify each term.

Apply the distributive property.

$y = - \frac{3}{2} \cdot - 8 - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$y = \frac{- 3}{2} \cdot - 8 - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Factor $2$ out of $- 8$ .

$y = \frac{- 3}{2} \cdot (2 (- 4)) - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Cancel the common factor.

$y = \frac{- 3}{2} \cdot (2 \cdot - 4) - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Rewrite the expression.

$y = - 3 \cdot - 4 - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

$y = - 3 \cdot - 4 - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Multiply $- 3$ by $- 4$ .

$y = 12 - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$y = 12 + \frac{- 3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

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

$y = 12 + \frac{- 3}{2} \cdot (2 (- y)) - 6$

$x = - 8 - 2 y$

Cancel the common factor.

$y = 12 + \frac{- 3}{2} \cdot (2 (- y)) - 6$

$x = - 8 - 2 y$

Rewrite the expression.

$y = 12 - 3 (- y) - 6$

$x = - 8 - 2 y$

$y = 12 - 3 (- y) - 6$

$x = - 8 - 2 y$

Multiply $- 1$ by $- 3$ .

$y = 12 + 3 y - 6$

$x = - 8 - 2 y$

$y = 12 + 3 y - 6$

$x = - 8 - 2 y$

Subtract $6$ from $12$ .

$y = 3 y + 6$

$x = - 8 - 2 y$

$y = 3 y + 6$

$x = - 8 - 2 y$

$y = 3 y + 6$

$x = - 8 - 2 y$

$y = 3 y + 6$

$x = - 8 - 2 y$

Solve for $y$ in $y = 3 y + 6$ .

Move all terms containing $y$ to the left side of the equation.

Subtract $3 y$ from both sides of the equation.

$y - 3 y = 6$

$x = - 8 - 2 y$

Subtract $3 y$ from $y$ .

$- 2 y = 6$

$x = - 8 - 2 y$

$- 2 y = 6$

$x = - 8 - 2 y$

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

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

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

$x = - 8 - 2 y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$x = - 8 - 2 y$

Divide $y$ by $1$ .

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

$x = - 8 - 2 y$

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

$x = - 8 - 2 y$

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

$x = - 8 - 2 y$

Simplify the right side.

Divide $6$ by $- 2$ .

$y = - 3$

$x = - 8 - 2 y$

$y = - 3$

$x = - 8 - 2 y$

$y = - 3$

$x = - 8 - 2 y$

$y = - 3$

$x = - 8 - 2 y$

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

Replace all occurrences of $y$ in $x = - 8 - 2 y$ with $- 3$ .

$x = - 8 - 2 \cdot - 3$

$y = - 3$

Simplify the right side.

Simplify $- 8 - 2 \cdot - 3$ .

Multiply $- 2$ by $- 3$ .

$x = - 8 + 6$

$y = - 3$

Add $- 8$ and $6$ .

$x = - 2$

$y = - 3$

$x = - 2$

$y = - 3$

$x = - 2$

$y = - 3$

$x = - 2$

$y = - 3$

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

$(- 2, - 3)$

The result can be shown in multiple forms.

Point Form:

$(- 2, - 3)$

Equation Form:

$x = - 2, y = - 3$

Solve the System of Equations x+2y=-8 y=-3/2x-6

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