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

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

Step 1

Eliminate the equal sides of each equation and combine.

$- x + 3 = x + 1$

Step 2

Solve $- x + 3 = x + 1$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$- x + 3 - x = 1$

Subtract $x$ from $- x$ .

$- 2 x + 3 = 1$

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

Subtract $3$ from both sides of the equation.

$- 2 x = 1 - 3$

Subtract $3$ from $1$ .

$- 2 x = - 2$

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 $x$ .

$y = (1) + 1$

Substitute $1$ for $x$ in $y = (1) + 1$ and solve for $y$ .

Remove parentheses.

$y = 1 + 1$

Remove parentheses.

$y = (1) + 1$

Add $1$ and $1$ .

$y = 2$

Step 4

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

$(1, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 2)$

Equation Form:

$x = 1, y = 2$

Step 6

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

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