Solve the System of Equations 9x-6y=-12 and 8x-5y=-8

$9 x - 6 y = - 12$ and $8 x - 5 y = - 8$

Step 1

Solve for $x$ in $9 x - 6 y = - 12$ .

Add $6 y$ to both sides of the equation.

$9 x = - 12 + 6 y$

$8 x - 5 y = - 8$

Divide each term in $9 x = - 12 + 6 y$ by $9$ and simplify.

Divide each term in $9 x = - 12 + 6 y$ by $9$ .

$\frac{9 x}{9} = \frac{- 12}{9} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 12}{9} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

Divide $x$ by $1$ .

$x = \frac{- 12}{9} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

$x = \frac{- 12}{9} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

$x = \frac{- 12}{9} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 12$ and $9$ .

Factor $3$ out of $- 12$ .

$x = \frac{3 (- 4)}{9} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

Cancel the common factors.

Factor $3$ out of $9$ .

$x = \frac{3 \cdot - 4}{3 \cdot 3} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

Cancel the common factor.

$x = \frac{3 \cdot - 4}{3 \cdot 3} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

Rewrite the expression.

$x = \frac{- 4}{3} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

$x = \frac{- 4}{3} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

$x = \frac{- 4}{3} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

Move the negative in front of the fraction.

$x = - \frac{4}{3} + \frac{6 y}{9}$

$8 x - 5 y = - 8$

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6 y$ .

$x = - \frac{4}{3} + \frac{3 (2 y)}{9}$

$8 x - 5 y = - 8$

Cancel the common factors.

Factor $3$ out of $9$ .

$x = - \frac{4}{3} + \frac{3 (2 y)}{3 (3)}$

$8 x - 5 y = - 8$

Cancel the common factor.

$x = - \frac{4}{3} + \frac{3 (2 y)}{3 \cdot 3}$

$8 x - 5 y = - 8$

Rewrite the expression.

$x = - \frac{4}{3} + \frac{2 y}{3}$

$8 x - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$8 x - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$8 x - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$8 x - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$8 x - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$8 x - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$8 x - 5 y = - 8$

Step 2

Replace all occurrences of $x$ with $- \frac{4}{3} + \frac{2 y}{3}$ in each equation.

Replace all occurrences of $x$ in $8 x - 5 y = - 8$ with $- \frac{4}{3} + \frac{2 y}{3}$ .

$8 (- \frac{4}{3} + \frac{2 y}{3}) - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Simplify the left side.

Simplify $8 (- \frac{4}{3} + \frac{2 y}{3}) - 5 y$ .

Simplify each term.

Apply the distributive property.

$8 (- \frac{4}{3}) + 8 (\frac{2 y}{3}) - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Multiply $8 (- \frac{4}{3})$ .

Multiply $- 1$ by $8$ .

$- 8 (\frac{4}{3}) + 8 (\frac{2 y}{3}) - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Combine $- 8$ and $\frac{4}{3}$ .

$\frac{- 8 \cdot 4}{3} + 8 (\frac{2 y}{3}) - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Multiply $- 8$ by $4$ .

$\frac{- 32}{3} + 8 (\frac{2 y}{3}) - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$\frac{- 32}{3} + 8 (\frac{2 y}{3}) - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Multiply $8 \frac{2 y}{3}$ .

Combine $8$ and $\frac{2 y}{3}$ .

$\frac{- 32}{3} + \frac{8 (2 y)}{3} - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Multiply $2$ by $8$ .

$\frac{- 32}{3} + \frac{16 y}{3} - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$\frac{- 32}{3} + \frac{16 y}{3} - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Move the negative in front of the fraction.

$- \frac{32}{3} + \frac{16 y}{3} - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$- \frac{32}{3} + \frac{16 y}{3} - 5 y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

To write $- 5 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{32}{3} + \frac{16 y}{3} - 5 y \cdot \frac{3}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Combine $- 5 y$ and $\frac{3}{3}$ .

$- \frac{32}{3} + \frac{16 y}{3} + \frac{- 5 y \cdot 3}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Combine the numerators over the common denominator.

$- \frac{32}{3} + \frac{16 y - 5 y \cdot 3}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Combine the numerators over the common denominator.

$\frac{- 32 + 16 y - 5 y \cdot 3}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Multiply $3$ by $- 5$ .

$\frac{- 32 + 16 y - 15 y}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Subtract $15 y$ from $16 y$ .

$\frac{- 32 + y}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Rewrite $- 32$ as $- 1 (32)$ .

$\frac{- 1 \cdot 32 + y}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Factor $- 1$ out of $y$ .

$\frac{- 1 \cdot 32 - 1 (- y)}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Factor $- 1$ out of $- 1 (32) - 1 (- y)$ .

$\frac{- 1 (32 - y)}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Move the negative in front of the fraction.

$- \frac{32 - y}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$- \frac{32 - y}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$- \frac{32 - y}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$- \frac{32 - y}{3} = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Step 3

Solve for $y$ in $- \frac{32 - y}{3} = - 8$ .

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{32 - y}{3}) = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{32 - y}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{32 - y}{3}$ into the numerator.

$- 3 \frac{- (32 - y)}{3} = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Factor $3$ out of $- 3$ .

$3 (- 1) (\frac{- (32 - y)}{3}) = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Cancel the common factor.

$3 \cdot (- 1 \frac{- (32 - y)}{3}) = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Rewrite the expression.

$32 - y = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$32 - y = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (32 - y) = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Multiply $32 - y$ by $1$ .

$32 - y = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$32 - y = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$32 - y = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$32 - y = - 3 \cdot - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Simplify the right side.

Multiply $- 3$ by $- 8$ .

$32 - y = 24$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$32 - y = 24$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$32 - y = 24$

$x = - \frac{4}{3} + \frac{2 y}{3}$

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

Subtract $32$ from both sides of the equation.

$- y = 24 - 32$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Subtract $32$ from $24$ .

$- y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$- y = - 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Divide each term in $- y = - 8$ by $- 1$ and simplify.

Divide each term in $- y = - 8$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 8}{- 1}$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 8}{- 1}$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Divide $y$ by $1$ .

$y = \frac{- 8}{- 1}$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$y = \frac{- 8}{- 1}$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Simplify the right side.

Divide $- 8$ by $- 1$ .

$y = 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$y = 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$y = 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

$y = 8$

$x = - \frac{4}{3} + \frac{2 y}{3}$

Step 4

Replace all occurrences of $y$ with $8$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{4}{3} + \frac{2 y}{3}$ with $8$ .

$x = - \frac{4}{3} + \frac{2 (8)}{3}$

$y = 8$

Simplify the right side.

Simplify $- \frac{4}{3} + \frac{2 (8)}{3}$ .

Combine the numerators over the common denominator.

$x = \frac{- 4 + 2 (8)}{3}$

$y = 8$

Simplify the expression.

Multiply $2$ by $8$ .

$x = \frac{- 4 + 16}{3}$

$y = 8$

Add $- 4$ and $16$ .

$x = \frac{12}{3}$

$y = 8$

Divide $12$ by $3$ .

$x = 4$

$y = 8$

$x = 4$

$y = 8$

$x = 4$

$y = 8$

$x = 4$

$y = 8$

$x = 4$

$y = 8$

Step 5

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

$(4, 8)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 8)$

Equation Form:

$x = 4, y = 8$

Step 7

Solve the System of Equations 9x-6y=-12 and 8x-5y=-8

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