Solve by Substitution x+y=-3 , x-y=1

$x + y = - 3$ , $x - y = 1$

Step 1

Subtract $y$ from both sides of the equation.

$x = - 3 - y$

$x - y = 1$

Step 2

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

Replace all occurrences of $x$ in $x - y = 1$ with $- 3 - y$ .

$(- 3 - y) - y = 1$

$x = - 3 - y$

Simplify the left side.

Subtract $y$ from $- y$ .

$- 3 - 2 y = 1$

$x = - 3 - y$

$- 3 - 2 y = 1$

$x = - 3 - y$

$- 3 - 2 y = 1$

$x = - 3 - y$

Step 3

Solve for $y$ in $- 3 - 2 y = 1$ .

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

Add $3$ to both sides of the equation.

$- 2 y = 1 + 3$

$x = - 3 - y$

Add $1$ and $3$ .

$- 2 y = 4$

$x = - 3 - y$

$- 2 y = 4$

$x = - 3 - y$

Divide each term in $- 2 y = 4$ by $- 2$ and simplify.

Divide each term in $- 2 y = 4$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{4}{- 2}$

$x = - 3 - y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{4}{- 2}$

$x = - 3 - y$

Divide $y$ by $1$ .

$y = \frac{4}{- 2}$

$x = - 3 - y$

$y = \frac{4}{- 2}$

$x = - 3 - y$

$y = \frac{4}{- 2}$

$x = - 3 - y$

Simplify the right side.

Divide $4$ by $- 2$ .

$y = - 2$

$x = - 3 - y$

$y = - 2$

$x = - 3 - y$

$y = - 2$

$x = - 3 - y$

$y = - 2$

$x = - 3 - y$

Step 4

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

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

$x = - 3 - (- 2)$

$y = - 2$

Simplify the right side.

Simplify $- 3 - (- 2)$ .

Multiply $- 1$ by $- 2$ .

$x = - 3 + 2$

$y = - 2$

Add $- 3$ and $2$ .

$x = - 1$

$y = - 2$

$x = - 1$

$y = - 2$

$x = - 1$

$y = - 2$

$x = - 1$

$y = - 2$

Step 5

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

$(- 1, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, - 2)$

Equation Form:

$x = - 1, y = - 2$

Step 7

Solve by Substitution x+y=-3 , x-y=1

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