Solve by Substitution x+y=-4 , x-y=2

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

Step 1

Subtract $y$ from both sides of the equation.

$x = - 4 - y$

$x - y = 2$

Step 2

Replace all occurrences of $x$ with $- 4 - y$ in each equation.

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

$(- 4 - y) - y = 2$

$x = - 4 - y$

Simplify the left side.

Subtract $y$ from $- y$ .

$- 4 - 2 y = 2$

$x = - 4 - y$

$- 4 - 2 y = 2$

$x = - 4 - y$

$- 4 - 2 y = 2$

$x = - 4 - y$

Step 3

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

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

Add $4$ to both sides of the equation.

$- 2 y = 2 + 4$

$x = - 4 - y$

Add $2$ and $4$ .

$- 2 y = 6$

$x = - 4 - y$

$- 2 y = 6$

$x = - 4 - y$

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

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

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

$x = - 4 - y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$x = - 4 - y$

Divide $y$ by $1$ .

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

$x = - 4 - y$

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

$x = - 4 - y$

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

$x = - 4 - y$

Simplify the right side.

Divide $6$ by $- 2$ .

$y = - 3$

$x = - 4 - y$

$y = - 3$

$x = - 4 - y$

$y = - 3$

$x = - 4 - y$

$y = - 3$

$x = - 4 - y$

Step 4

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

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

$x = - 4 - (- 3)$

$y = - 3$

Simplify the right side.

Simplify $- 4 - (- 3)$ .

Multiply $- 1$ by $- 3$ .

$x = - 4 + 3$

$y = - 3$

Add $- 4$ and $3$ .

$x = - 1$

$y = - 3$

$x = - 1$

$y = - 3$

$x = - 1$

$y = - 3$

$x = - 1$

$y = - 3$

Step 5

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

$(- 1, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, - 3)$

Equation Form:

$x = - 1, y = - 3$

Step 7

Solve by Substitution x+y=-4 , x-y=2

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