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.

Subtract $4$ from both sides of the equation.

$- 2 y = - 2 - 4$

$x = 4 - y$

Subtract $4$ from $- 2$ .

$- 2 y = - 6$

$x = 4 - y$

$- 2 y = - 6$

$x = 4 - y$

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 $3$ .

$x = 4 - 3$

$y = 3$

Subtract $3$ from $4$ .

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

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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