Solve by Substitution y=5x+8 , y=8x+9

$y = 5 x + 8$ , $y = 8 x + 9$

Step 1

Eliminate the equal sides of each equation and combine.

$5 x + 8 = 8 x + 9$

Step 2

Solve $5 x + 8 = 8 x + 9$ for $x$ .

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

Subtract $8 x$ from both sides of the equation.

$5 x + 8 - 8 x = 9$

Subtract $8 x$ from $5 x$ .

$- 3 x + 8 = 9$

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

Subtract $8$ from both sides of the equation.

$- 3 x = 9 - 8$

Subtract $8$ from $9$ .

$- 3 x = 1$

Divide each term in $- 3 x = 1$ by $- 3$ and simplify.

Divide each term in $- 3 x = 1$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{1}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{1}{- 3}$

Divide $x$ by $1$ .

$x = \frac{1}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

Step 3

Evaluate $y$ when $x = - \frac{1}{3}$ .

Substitute $- \frac{1}{3}$ for $x$ .

$y = 8 (- \frac{1}{3}) + 9$

Simplify $8 (- \frac{1}{3}) + 9$ .

Simplify each term.

Multiply $8 (- \frac{1}{3})$ .

Multiply $- 1$ by $8$ .

$y = - 8 (\frac{1}{3}) + 9$

Combine $- 8$ and $\frac{1}{3}$ .

$y = \frac{- 8}{3} + 9$

Move the negative in front of the fraction.

$y = - \frac{8}{3} + 9$

To write $9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{8}{3} + 9 \cdot \frac{3}{3}$

Combine $9$ and $\frac{3}{3}$ .

$y = - \frac{8}{3} + \frac{9 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 8 + 9 \cdot 3}{3}$

Simplify the numerator.

Multiply $9$ by $3$ .

$y = \frac{- 8 + 27}{3}$

Add $- 8$ and $27$ .

$y = \frac{19}{3}$

Step 4

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

$(- \frac{1}{3}, \frac{19}{3})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- \frac{1}{3}, \frac{19}{3})$

Equation Form:

$x = - \frac{1}{3}, y = \frac{19}{3}$

Step 6

Solve by Substitution y=5x+8 , y=8x+9

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