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

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

Step 1

Subtract $y$ from both sides of the equation.

$x = 2 - y$

$x - y = 4$

Step 2

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

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

$(2 - y) - y = 4$

$x = 2 - y$

Simplify the left side.

Subtract $y$ from $- y$ .

$2 - 2 y = 4$

$x = 2 - y$

$2 - 2 y = 4$

$x = 2 - y$

$2 - 2 y = 4$

$x = 2 - y$

Step 3

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

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

Subtract $2$ from both sides of the equation.

$- 2 y = 4 - 2$

$x = 2 - y$

Subtract $2$ from $4$ .

$- 2 y = 2$

$x = 2 - y$

$- 2 y = 2$

$x = 2 - y$

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

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

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

$x = 2 - y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$x = 2 - y$

Divide $y$ by $1$ .

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

$x = 2 - y$

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

$x = 2 - y$

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

$x = 2 - y$

Simplify the right side.

Divide $2$ by $- 2$ .

$y = - 1$

$x = 2 - y$

$y = - 1$

$x = 2 - y$

$y = - 1$

$x = 2 - y$

$y = - 1$

$x = 2 - y$

Step 4

Replace all occurrences of $y$ with $- 1$ in each equation.

Replace all occurrences of $y$ in $x = 2 - y$ with $- 1$ .

$x = 2 - (- 1)$

$y = - 1$

Simplify the right side.

Simplify $2 - (- 1)$ .

Multiply $- 1$ by $- 1$ .

$x = 2 + 1$

$y = - 1$

Add $2$ and $1$ .

$x = 3$

$y = - 1$

$x = 3$

$y = - 1$

$x = 3$

$y = - 1$

$x = 3$

$y = - 1$

Step 5

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

$(3, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, - 1)$

Equation Form:

$x = 3, y = - 1$

Step 7

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

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