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

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

Step 1

Eliminate the equal sides of each equation and combine.

$x = - x + 2$

Step 2

Solve $x = - x + 2$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$x + x = 2$

Add $x$ and $x$ .

$2 x = 2$

Divide each term in $2 x = 2$ by $2$ and simplify.

Divide each term in $2 x = 2$ by $2$ .

$\frac{2 x}{2} = \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{2}{2}$

Divide $x$ by $1$ .

$x = \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$x = 1$

Step 3

Evaluate $y$ when $x = 1$ .

Substitute $1$ for $x$ .

$y = - (1) + 2$

Simplify $- (1) + 2$ .

Multiply $- 1$ by $1$ .

$y = - 1 + 2$

Add $- 1$ and $2$ .

$y = 1$

Step 4

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

$(1, 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 1)$

Equation Form:

$x = 1, y = 1$

Step 6