Solve by Substitution -7x-8y=9 , -4x+9y=-22

$- 7 x - 8 y = 9$ , $- 4 x + 9 y = - 22$

Step 1

Solve for $x$ in $- 7 x - 8 y = 9$ .

Add $8 y$ to both sides of the equation.

$- 7 x = 9 + 8 y$

$- 4 x + 9 y = - 22$

Divide each term in $- 7 x = 9 + 8 y$ by $- 7$ and simplify.

Divide each term in $- 7 x = 9 + 8 y$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{9}{- 7} + \frac{8 y}{- 7}$

$- 4 x + 9 y = - 22$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{9}{- 7} + \frac{8 y}{- 7}$

$- 4 x + 9 y = - 22$

Divide $x$ by $1$ .

$x = \frac{9}{- 7} + \frac{8 y}{- 7}$

$- 4 x + 9 y = - 22$

$x = \frac{9}{- 7} + \frac{8 y}{- 7}$

$- 4 x + 9 y = - 22$

$x = \frac{9}{- 7} + \frac{8 y}{- 7}$

$- 4 x + 9 y = - 22$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{9}{7} + \frac{8 y}{- 7}$

$- 4 x + 9 y = - 22$

Move the negative in front of the fraction.

$x = - \frac{9}{7} - \frac{8 y}{7}$

$- 4 x + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$- 4 x + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$- 4 x + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$- 4 x + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$- 4 x + 9 y = - 22$

Step 2

Replace all occurrences of $x$ with $- \frac{9}{7} - \frac{8 y}{7}$ in each equation.

Replace all occurrences of $x$ in $- 4 x + 9 y = - 22$ with $- \frac{9}{7} - \frac{8 y}{7}$ .

$- 4 (- \frac{9}{7} - \frac{8 y}{7}) + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Simplify the left side.

Simplify $- 4 (- \frac{9}{7} - \frac{8 y}{7}) + 9 y$ .

Simplify each term.

Apply the distributive property.

$- 4 (- \frac{9}{7}) - 4 (- \frac{8 y}{7}) + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Multiply $- 4 (- \frac{9}{7})$ .

Multiply $- 1$ by $- 4$ .

$4 (\frac{9}{7}) - 4 (- \frac{8 y}{7}) + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Combine $4$ and $\frac{9}{7}$ .

$\frac{4 \cdot 9}{7} - 4 (- \frac{8 y}{7}) + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Multiply $4$ by $9$ .

$\frac{36}{7} - 4 (- \frac{8 y}{7}) + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$\frac{36}{7} - 4 (- \frac{8 y}{7}) + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Multiply $- 4 (- \frac{8 y}{7})$ .

Multiply $- 1$ by $- 4$ .

$\frac{36}{7} + 4 (\frac{8 y}{7}) + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Combine $4$ and $\frac{8 y}{7}$ .

$\frac{36}{7} + \frac{4 (8 y)}{7} + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Multiply $8$ by $4$ .

$\frac{36}{7} + \frac{32 y}{7} + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$\frac{36}{7} + \frac{32 y}{7} + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$\frac{36}{7} + \frac{32 y}{7} + 9 y = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

To write $9 y$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{36}{7} + \frac{32 y}{7} + 9 y \cdot \frac{7}{7} = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Combine $9 y$ and $\frac{7}{7}$ .

$\frac{36}{7} + \frac{32 y}{7} + \frac{9 y \cdot 7}{7} = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Combine the numerators over the common denominator.

$\frac{36}{7} + \frac{32 y + 9 y \cdot 7}{7} = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Combine the numerators over the common denominator.

$\frac{36 + 32 y + 9 y \cdot 7}{7} = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Multiply $7$ by $9$ .

$\frac{36 + 32 y + 63 y}{7} = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Add $32 y$ and $63 y$ .

$\frac{36 + 95 y}{7} = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$\frac{36 + 95 y}{7} = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$\frac{36 + 95 y}{7} = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$\frac{36 + 95 y}{7} = - 22$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Step 3

Solve for $y$ in $\frac{36 + 95 y}{7} = - 22$ .

Multiply both sides by $7$ .

$\frac{36 + 95 y}{7} \cdot 7 = - 22 \cdot 7$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Simplify.

Simplify the left side.

Simplify $\frac{36 + 95 y}{7} \cdot 7$ .

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{36 + 95 y}{7} \cdot 7 = - 22 \cdot 7$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Rewrite the expression.

$36 + 95 y = - 22 \cdot 7$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$36 + 95 y = - 22 \cdot 7$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Reorder $36$ and $95 y$ .

$95 y + 36 = - 22 \cdot 7$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$95 y + 36 = - 22 \cdot 7$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$95 y + 36 = - 22 \cdot 7$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Simplify the right side.

Multiply $- 22$ by $7$ .

$95 y + 36 = - 154$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$95 y + 36 = - 154$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$95 y + 36 = - 154$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Solve for $y$ .

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

Subtract $36$ from both sides of the equation.

$95 y = - 154 - 36$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Subtract $36$ from $- 154$ .

$95 y = - 190$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$95 y = - 190$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Divide each term in $95 y = - 190$ by $95$ and simplify.

Divide each term in $95 y = - 190$ by $95$ .

$\frac{95 y}{95} = \frac{- 190}{95}$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Simplify the left side.

Cancel the common factor of $95$ .

Cancel the common factor.

$\frac{95 y}{95} = \frac{- 190}{95}$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Divide $y$ by $1$ .

$y = \frac{- 190}{95}$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$y = \frac{- 190}{95}$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$y = \frac{- 190}{95}$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Simplify the right side.

Divide $- 190$ by $95$ .

$y = - 2$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$y = - 2$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$y = - 2$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$y = - 2$

$x = - \frac{9}{7} - \frac{8 y}{7}$

$y = - 2$

$x = - \frac{9}{7} - \frac{8 y}{7}$

Step 4

Replace all occurrences of $y$ with $- 2$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{9}{7} - \frac{8 y}{7}$ with $- 2$ .

$x = - \frac{9}{7} - \frac{8 (- 2)}{7}$

$y = - 2$

Simplify the right side.

Simplify $- \frac{9}{7} - \frac{8 (- 2)}{7}$ .

Combine the numerators over the common denominator.

$x = \frac{- 9 - 8 \cdot - 2}{7}$

$y = - 2$

Simplify the expression.

Multiply $- 8$ by $- 2$ .

$x = \frac{- 9 + 16}{7}$

$y = - 2$

Add $- 9$ and $16$ .

$x = \frac{7}{7}$

$y = - 2$

Divide $7$ by $7$ .

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

Step 5

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

$(1, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, - 2)$

Equation Form:

$x = 1, y = - 2$

Step 7

Solve by Substitution -7x-8y=9 , -4x+9y=-22

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