Solve by Substitution y=3x+7 , y=5x+8

$y = 3 x + 7$ , $y = 5 x + 8$

Step 1

Eliminate the equal sides of each equation and combine.

$3 x + 7 = 5 x + 8$

Step 2

Solve $3 x + 7 = 5 x + 8$ for $x$ .

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

Subtract $5 x$ from both sides of the equation.

$3 x + 7 - 5 x = 8$

Subtract $5 x$ from $3 x$ .

$- 2 x + 7 = 8$

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

Subtract $7$ from both sides of the equation.

$- 2 x = 8 - 7$

Subtract $7$ from $8$ .

$- 2 x = 1$

Divide each term in $- 2 x = 1$ by $- 2$ and simplify.

Divide each term in $- 2 x = 1$ by $- 2$ .

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

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 $x$ .

$y = 5 (- \frac{1}{2}) + 8$

Simplify $5 (- \frac{1}{2}) + 8$ .

Simplify each term.

Multiply $5 (- \frac{1}{2})$ .

Multiply $- 1$ by $5$ .

$y = - 5 (\frac{1}{2}) + 8$

Combine $- 5$ and $\frac{1}{2}$ .

$y = \frac{- 5}{2} + 8$

Move the negative in front of the fraction.

$y = - \frac{5}{2} + 8$

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{5}{2} + 8 \cdot \frac{2}{2}$

Combine $8$ and $\frac{2}{2}$ .

$y = - \frac{5}{2} + \frac{8 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{- 5 + 8 \cdot 2}{2}$

Simplify the numerator.

Multiply $8$ by $2$ .

$y = \frac{- 5 + 16}{2}$

Add $- 5$ and $16$ .

$y = \frac{11}{2}$

Step 4

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

$(- \frac{1}{2}, \frac{11}{2})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- \frac{1}{2}, \frac{11}{2})$

Equation Form:

$x = - \frac{1}{2}, y = \frac{11}{2}$

Step 6

Solve by Substitution y=3x+7 , y=5x+8

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