Solve by Substitution y=5x+6 , y=9x+7

$y = 5 x + 6$ , $y = 9 x + 7$

Step 1

Eliminate the equal sides of each equation and combine.

$5 x + 6 = 9 x + 7$

Step 2

Solve $5 x + 6 = 9 x + 7$ for $x$ .

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

Subtract $9 x$ from both sides of the equation.

$5 x + 6 - 9 x = 7$

Subtract $9 x$ from $5 x$ .

$- 4 x + 6 = 7$

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

Subtract $6$ from both sides of the equation.

$- 4 x = 7 - 6$

Subtract $6$ from $7$ .

$- 4 x = 1$

Divide each term in $- 4 x = 1$ by $- 4$ and simplify.

Divide each term in $- 4 x = 1$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{1}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{1}{- 4}$

Divide $x$ by $1$ .

$x = \frac{1}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{4}$

Step 3

Evaluate $y$ when $x = - \frac{1}{4}$ .

Substitute $- \frac{1}{4}$ for $x$ .

$y = 9 (- \frac{1}{4}) + 7$

Simplify $9 (- \frac{1}{4}) + 7$ .

Simplify each term.

Multiply $9 (- \frac{1}{4})$ .

Multiply $- 1$ by $9$ .

$y = - 9 (\frac{1}{4}) + 7$

Combine $- 9$ and $\frac{1}{4}$ .

$y = \frac{- 9}{4} + 7$

Move the negative in front of the fraction.

$y = - \frac{9}{4} + 7$

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{9}{4} + 7 \cdot \frac{4}{4}$

Combine $7$ and $\frac{4}{4}$ .

$y = - \frac{9}{4} + \frac{7 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{- 9 + 7 \cdot 4}{4}$

Simplify the numerator.

Multiply $7$ by $4$ .

$y = \frac{- 9 + 28}{4}$

Add $- 9$ and $28$ .

$y = \frac{19}{4}$

Step 4

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

$(- \frac{1}{4}, \frac{19}{4})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- \frac{1}{4}, \frac{19}{4})$

Equation Form:

$x = - \frac{1}{4}, y = \frac{19}{4}$

Step 6

Solve by Substitution y=5x+6 , y=9x+7

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