Solve the System of Equations -2x-9y=8 and -5x-8y=-9

$- 2 x - 9 y = 8$ and $- 5 x - 8 y = - 9$

Step 1

Solve for $x$ in $- 2 x - 9 y = 8$ .

Add $9 y$ to both sides of the equation.

$- 2 x = 8 + 9 y$

$- 5 x - 8 y = - 9$

Divide each term in $- 2 x = 8 + 9 y$ by $- 2$ and simplify.

Divide each term in $- 2 x = 8 + 9 y$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{8}{- 2} + \frac{9 y}{- 2}$

$- 5 x - 8 y = - 9$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{8}{- 2} + \frac{9 y}{- 2}$

$- 5 x - 8 y = - 9$

Divide $x$ by $1$ .

$x = \frac{8}{- 2} + \frac{9 y}{- 2}$

$- 5 x - 8 y = - 9$

$x = \frac{8}{- 2} + \frac{9 y}{- 2}$

$- 5 x - 8 y = - 9$

$x = \frac{8}{- 2} + \frac{9 y}{- 2}$

$- 5 x - 8 y = - 9$

Simplify the right side.

Simplify each term.

Divide $8$ by $- 2$ .

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

$- 5 x - 8 y = - 9$

Move the negative in front of the fraction.

$x = - 4 - \frac{9 y}{2}$

$- 5 x - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

$- 5 x - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

$- 5 x - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

$- 5 x - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

$- 5 x - 8 y = - 9$

Step 2

Replace all occurrences of $x$ with $- 4 - \frac{9 y}{2}$ in each equation.

Replace all occurrences of $x$ in $- 5 x - 8 y = - 9$ with $- 4 - \frac{9 y}{2}$ .

$- 5 (- 4 - \frac{9 y}{2}) - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

Simplify the left side.

Simplify $- 5 (- 4 - \frac{9 y}{2}) - 8 y$ .

Simplify each term.

Apply the distributive property.

$- 5 \cdot - 4 - 5 (- \frac{9 y}{2}) - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

Multiply $- 5$ by $- 4$ .

$20 - 5 (- \frac{9 y}{2}) - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

Multiply $- 5 (- \frac{9 y}{2})$ .

Multiply $- 1$ by $- 5$ .

$20 + 5 (\frac{9 y}{2}) - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

Combine $5$ and $\frac{9 y}{2}$ .

$20 + \frac{5 (9 y)}{2} - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

Multiply $9$ by $5$ .

$20 + \frac{45 y}{2} - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

$20 + \frac{45 y}{2} - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

$20 + \frac{45 y}{2} - 8 y = - 9$

$x = - 4 - \frac{9 y}{2}$

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

$20 + \frac{45 y}{2} - 8 y \cdot \frac{2}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

Simplify terms.

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

$20 + \frac{45 y}{2} + \frac{- 8 y \cdot 2}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

Combine the numerators over the common denominator.

$20 + \frac{45 y - 8 y \cdot 2}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

$20 + \frac{45 y - 8 y \cdot 2}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

Simplify each term.

Simplify the numerator.

Factor $y$ out of $45 y - 8 y \cdot 2$ .

Factor $y$ out of $45 y$ .

$20 + \frac{y \cdot 45 - 8 y \cdot 2}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

Factor $y$ out of $- 8 y \cdot 2$ .

$20 + \frac{y \cdot 45 + y (- 8 \cdot 2)}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

Factor $y$ out of $y \cdot 45 + y (- 8 \cdot 2)$ .

$20 + \frac{y (45 - 8 \cdot 2)}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

$20 + \frac{y (45 - 8 \cdot 2)}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

Multiply $- 8$ by $2$ .

$20 + \frac{y (45 - 16)}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

Subtract $16$ from $45$ .

$20 + \frac{y \cdot 29}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

$20 + \frac{y \cdot 29}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

Move $29$ to the left of $y$ .

$20 + \frac{29 y}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

$20 + \frac{29 y}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

$20 + \frac{29 y}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

$20 + \frac{29 y}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

$20 + \frac{29 y}{2} = - 9$

$x = - 4 - \frac{9 y}{2}$

Step 3

Solve for $y$ in $20 + \frac{29 y}{2} = - 9$ .

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

Subtract $20$ from both sides of the equation.

$\frac{29 y}{2} = - 9 - 20$

$x = - 4 - \frac{9 y}{2}$

Subtract $20$ from $- 9$ .

$\frac{29 y}{2} = - 29$

$x = - 4 - \frac{9 y}{2}$

$\frac{29 y}{2} = - 29$

$x = - 4 - \frac{9 y}{2}$

Multiply both sides of the equation by $\frac{2}{29}$ .

$\frac{2}{29} \cdot \frac{29 y}{2} = \frac{2}{29} \cdot - 29$

$x = - 4 - \frac{9 y}{2}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{29} \cdot \frac{29 y}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{29} \cdot \frac{29 y}{2} = \frac{2}{29} \cdot - 29$

$x = - 4 - \frac{9 y}{2}$

Rewrite the expression.

$\frac{1}{29} \cdot (29 y) = \frac{2}{29} \cdot - 29$

$x = - 4 - \frac{9 y}{2}$

$\frac{1}{29} \cdot (29 y) = \frac{2}{29} \cdot - 29$

$x = - 4 - \frac{9 y}{2}$

Cancel the common factor of $29$ .

Factor $29$ out of $29 y$ .

$\frac{1}{29} \cdot (29 (y)) = \frac{2}{29} \cdot - 29$

$x = - 4 - \frac{9 y}{2}$

Cancel the common factor.

$\frac{1}{29} \cdot (29 y) = \frac{2}{29} \cdot - 29$

$x = - 4 - \frac{9 y}{2}$

Rewrite the expression.

$y = \frac{2}{29} \cdot - 29$

$x = - 4 - \frac{9 y}{2}$

$y = \frac{2}{29} \cdot - 29$

$x = - 4 - \frac{9 y}{2}$

$y = \frac{2}{29} \cdot - 29$

$x = - 4 - \frac{9 y}{2}$

$y = \frac{2}{29} \cdot - 29$

$x = - 4 - \frac{9 y}{2}$

Simplify the right side.

Simplify $\frac{2}{29} \cdot - 29$ .

Cancel the common factor of $29$ .

Factor $29$ out of $- 29$ .

$y = \frac{2}{29} \cdot (29 (- 1))$

$x = - 4 - \frac{9 y}{2}$

Cancel the common factor.

$y = \frac{2}{29} \cdot (29 \cdot - 1)$

$x = - 4 - \frac{9 y}{2}$

Rewrite the expression.

$y = 2 \cdot - 1$

$x = - 4 - \frac{9 y}{2}$

$y = 2 \cdot - 1$

$x = - 4 - \frac{9 y}{2}$

Multiply $2$ by $- 1$ .

$y = - 2$

$x = - 4 - \frac{9 y}{2}$

$y = - 2$

$x = - 4 - \frac{9 y}{2}$

$y = - 2$

$x = - 4 - \frac{9 y}{2}$

$y = - 2$

$x = - 4 - \frac{9 y}{2}$

$y = - 2$

$x = - 4 - \frac{9 y}{2}$

Step 4

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

Replace all occurrences of $y$ in $x = - 4 - \frac{9 y}{2}$ with $- 2$ .

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

$y = - 2$

Simplify the right side.

Simplify $- 4 - \frac{9 (- 2)}{2}$ .

Simplify each term.

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $9 (- 2)$ .

$x = - 4 - \frac{2 (9 \cdot (- 1))}{2}$

$y = - 2$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = - 4 - \frac{2 (9 \cdot (- 1))}{2 (1)}$

$y = - 2$

Cancel the common factor.

$x = - 4 - \frac{2 (9 \cdot (- 1))}{2 \cdot 1}$

$y = - 2$

Rewrite the expression.

$x = - 4 - \frac{9 \cdot (- 1)}{1}$

$y = - 2$

Divide $9 \cdot (- 1)$ by $1$ .

$x = - 4 - (9 \cdot (- 1))$

$y = - 2$

$x = - 4 - (9 \cdot (- 1))$

$y = - 2$

$x = - 4 - (9 \cdot (- 1))$

$y = - 2$

Multiply $- (9 \cdot (- 1))$ .

Multiply $9$ by $- 1$ .

$x = - 4 + 9$

$y = - 2$

Multiply $- 1$ by $- 9$ .

$x = - 4 + 9$

$y = - 2$

$x = - 4 + 9$

$y = - 2$

$x = - 4 + 9$

$y = - 2$

Add $- 4$ and $9$ .

$x = 5$

$y = - 2$

$x = 5$

$y = - 2$

$x = 5$

$y = - 2$

$x = 5$

$y = - 2$

Step 5

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

$(5, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, - 2)$

Equation Form:

$x = 5, y = - 2$

Step 7

Solve the System of Equations -2x-9y=8 and -5x-8y=-9

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