Solve the System of Equations -x+2y=-9 and -5x+8y=-27

$- x + 2 y = - 9$ and $- 5 x + 8 y = - 27$

Step 1

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

Subtract $2 y$ from both sides of the equation.

$- x = - 9 - 2 y$

$- 5 x + 8 y = - 27$

Divide each term in $- x = - 9 - 2 y$ by $- 1$ and simplify.

Divide each term in $- x = - 9 - 2 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 9}{- 1} + \frac{- 2 y}{- 1}$

$- 5 x + 8 y = - 27$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 9}{- 1} + \frac{- 2 y}{- 1}$

$- 5 x + 8 y = - 27$

Divide $x$ by $1$ .

$x = \frac{- 9}{- 1} + \frac{- 2 y}{- 1}$

$- 5 x + 8 y = - 27$

$x = \frac{- 9}{- 1} + \frac{- 2 y}{- 1}$

$- 5 x + 8 y = - 27$

Simplify the right side.

Simplify each term.

Divide $- 9$ by $- 1$ .

$x = 9 + \frac{- 2 y}{- 1}$

$- 5 x + 8 y = - 27$

Move the negative one from the denominator of $\frac{- 2 y}{- 1}$ .

$x = 9 - 1 \cdot (- 2 y)$

$- 5 x + 8 y = - 27$

Rewrite $- 1 \cdot (- 2 y)$ as $- (- 2 y)$ .

$x = 9 - (- 2 y)$

$- 5 x + 8 y = - 27$

Multiply $- 2$ by $- 1$ .

$x = 9 + 2 y$

$- 5 x + 8 y = - 27$

$x = 9 + 2 y$

$- 5 x + 8 y = - 27$

$x = 9 + 2 y$

$- 5 x + 8 y = - 27$

$x = 9 + 2 y$

$- 5 x + 8 y = - 27$

$x = 9 + 2 y$

$- 5 x + 8 y = - 27$

Step 2

Replace all occurrences of $x$ with $9 + 2 y$ in each equation.

Replace all occurrences of $x$ in $- 5 x + 8 y = - 27$ with $9 + 2 y$ .

$- 5 (9 + 2 y) + 8 y = - 27$

$x = 9 + 2 y$

Simplify the left side.

Simplify $- 5 (9 + 2 y) + 8 y$ .

Simplify each term.

Apply the distributive property.

$- 5 \cdot 9 - 5 (2 y) + 8 y = - 27$

$x = 9 + 2 y$

Multiply $- 5$ by $9$ .

$- 45 - 5 (2 y) + 8 y = - 27$

$x = 9 + 2 y$

Multiply $2$ by $- 5$ .

$- 45 - 10 y + 8 y = - 27$

$x = 9 + 2 y$

$- 45 - 10 y + 8 y = - 27$

$x = 9 + 2 y$

Add $- 10 y$ and $8 y$ .

$- 45 - 2 y = - 27$

$x = 9 + 2 y$

$- 45 - 2 y = - 27$

$x = 9 + 2 y$

$- 45 - 2 y = - 27$

$x = 9 + 2 y$

$- 45 - 2 y = - 27$

$x = 9 + 2 y$

Step 3

Solve for $y$ in $- 45 - 2 y = - 27$ .

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

Add $45$ to both sides of the equation.

$- 2 y = - 27 + 45$

$x = 9 + 2 y$

Add $- 27$ and $45$ .

$- 2 y = 18$

$x = 9 + 2 y$

$- 2 y = 18$

$x = 9 + 2 y$

Divide each term in $- 2 y = 18$ by $- 2$ and simplify.

Divide each term in $- 2 y = 18$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{18}{- 2}$

$x = 9 + 2 y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{18}{- 2}$

$x = 9 + 2 y$

Divide $y$ by $1$ .

$y = \frac{18}{- 2}$

$x = 9 + 2 y$

$y = \frac{18}{- 2}$

$x = 9 + 2 y$

$y = \frac{18}{- 2}$

$x = 9 + 2 y$

Simplify the right side.

Divide $18$ by $- 2$ .

$y = - 9$

$x = 9 + 2 y$

$y = - 9$

$x = 9 + 2 y$

$y = - 9$

$x = 9 + 2 y$

$y = - 9$

$x = 9 + 2 y$

Step 4

Replace all occurrences of $y$ with $- 9$ in each equation.

Replace all occurrences of $y$ in $x = 9 + 2 y$ with $- 9$ .

$x = 9 + 2 (- 9)$

$y = - 9$

Simplify the right side.

Simplify $9 + 2 (- 9)$ .

Multiply $2$ by $- 9$ .

$x = 9 - 18$

$y = - 9$

Subtract $18$ from $9$ .

$x = - 9$

$y = - 9$

$x = - 9$

$y = - 9$

$x = - 9$

$y = - 9$

$x = - 9$

$y = - 9$

Step 5

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

$(- 9, - 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 9, - 9)$

Equation Form:

$x = - 9, y = - 9$

Step 7

Solve the System of Equations -x+2y=-9 and -5x+8y=-27

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