Solve by Substitution y=3x+5 , y=-x+3

$y = 3 x + 5$ , $y = - x + 3$

Step 1

Eliminate the equal sides of each equation and combine.

$3 x + 5 = - x + 3$

Step 2

Solve $3 x + 5 = - x + 3$ for $x$ .

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

Add $x$ to both sides of the equation.

$3 x + 5 + x = 3$

Add $3 x$ and $x$ .

$4 x + 5 = 3$

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

Subtract $5$ from both sides of the equation.

$4 x = 3 - 5$

Subtract $5$ from $3$ .

$4 x = - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2$ .

$x = \frac{2 (- 1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 1}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot - 1}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{- 1}{2}$

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 3

Evaluate $y$ when $x = - \frac{1}{2}$ .

Substitute $- \frac{1}{2}$ for $x$ .

$y = - (- \frac{1}{2}) + 3$

Substitute $- \frac{1}{2}$ for $x$ in $y = - (- \frac{1}{2}) + 3$ and solve for $y$ .

Multiply $- 1$ by $- \frac{1}{2}$ .

$y = \frac{1}{2} + 3$

Simplify $\frac{1}{2} + 3$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{1}{2} + 3 \cdot \frac{2}{2}$

Combine $3$ and $\frac{2}{2}$ .

$y = \frac{1}{2} + \frac{3 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{1 + 3 \cdot 2}{2}$

Simplify the numerator.

Multiply $3$ by $2$ .

$y = \frac{1 + 6}{2}$

Add $1$ and $6$ .

$y = \frac{7}{2}$

Step 4

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

$(- \frac{1}{2}, \frac{7}{2})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- \frac{1}{2}, \frac{7}{2})$

Equation Form:

$x = - \frac{1}{2}, y = \frac{7}{2}$

Step 6

Solve by Substitution y=3x+5 , y=-x+3

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