Solve the System of Equations x+2y=-3 x-y=-12

$x + 2 y = - 3$ $x - y = - 12$

Step 1

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

$x = - 3 - 2 y$

$x - y = - 12$

Step 2

Replace all occurrences of $x$ with $- 3 - 2 y$ in each equation.

Replace all occurrences of $x$ in $x - y = - 12$ with $- 3 - 2 y$ .

$(- 3 - 2 y) - y = - 12$

$x = - 3 - 2 y$

Simplify the left side.

Subtract $y$ from $- 2 y$ .

$- 3 - 3 y = - 12$

$x = - 3 - 2 y$

$- 3 - 3 y = - 12$

$x = - 3 - 2 y$

$- 3 - 3 y = - 12$

$x = - 3 - 2 y$

Step 3

Solve for $y$ in $- 3 - 3 y = - 12$ .

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

Add $3$ to both sides of the equation.

$- 3 y = - 12 + 3$

$x = - 3 - 2 y$

Add $- 12$ and $3$ .

$- 3 y = - 9$

$x = - 3 - 2 y$

$- 3 y = - 9$

$x = - 3 - 2 y$

Divide each term in $- 3 y = - 9$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 9$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 9}{- 3}$

$x = - 3 - 2 y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 9}{- 3}$

$x = - 3 - 2 y$

Divide $y$ by $1$ .

$y = \frac{- 9}{- 3}$

$x = - 3 - 2 y$

$y = \frac{- 9}{- 3}$

$x = - 3 - 2 y$

$y = \frac{- 9}{- 3}$

$x = - 3 - 2 y$

Simplify the right side.

Divide $- 9$ by $- 3$ .

$y = 3$

$x = - 3 - 2 y$

$y = 3$

$x = - 3 - 2 y$

$y = 3$

$x = - 3 - 2 y$

$y = 3$

$x = - 3 - 2 y$

Step 4

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

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

$x = - 3 - 2 \cdot 3$

$y = 3$

Simplify the right side.

Simplify $- 3 - 2 \cdot 3$ .

Multiply $- 2$ by $3$ .

$x = - 3 - 6$

$y = 3$

Subtract $6$ from $- 3$ .

$x = - 9$

$y = 3$

$x = - 9$

$y = 3$

$x = - 9$

$y = 3$

$x = - 9$

$y = 3$

Step 5

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

$(- 9, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 9, 3)$

Equation Form:

$x = - 9, y = 3$

Step 7

Solve the System of Equations x+2y=-3 x-y=-12

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