Solve the System of Equations -x+2y=-11 and 5x-8y=39

$- x + 2 y = - 11$ and $5 x - 8 y = 39$

Solve for $x$ in $- x + 2 y = - 11$ .

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

$- x = - 11 - 2 y$

$5 x - 8 y = 39$

Divide each term in $- x = - 11 - 2 y$ by $- 1$ and simplify.

Divide each term in $- x = - 11 - 2 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 11}{- 1} + \frac{- 2 y}{- 1}$

$5 x - 8 y = 39$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 11}{- 1} + \frac{- 2 y}{- 1}$

$5 x - 8 y = 39$

Divide $x$ by $1$ .

$x = \frac{- 11}{- 1} + \frac{- 2 y}{- 1}$

$5 x - 8 y = 39$

$x = \frac{- 11}{- 1} + \frac{- 2 y}{- 1}$

$5 x - 8 y = 39$

Simplify the right side.

Simplify each term.

Divide $- 11$ by $- 1$ .

$x = 11 + \frac{- 2 y}{- 1}$

$5 x - 8 y = 39$

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

$x = 11 - 1 \cdot (- 2 y)$

$5 x - 8 y = 39$

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

$x = 11 - (- 2 y)$

$5 x - 8 y = 39$

Multiply $- 2$ by $- 1$ .

$x = 11 + 2 y$

$5 x - 8 y = 39$

$x = 11 + 2 y$

$5 x - 8 y = 39$

$x = 11 + 2 y$

$5 x - 8 y = 39$

$x = 11 + 2 y$

$5 x - 8 y = 39$

$x = 11 + 2 y$

$5 x - 8 y = 39$

Replace all occurrences of $x$ with $11 + 2 y$ in each equation.

Replace all occurrences of $x$ in $5 x - 8 y = 39$ with $11 + 2 y$ .

$5 (11 + 2 y) - 8 y = 39$

$x = 11 + 2 y$

Simplify the left side.

Simplify $5 (11 + 2 y) - 8 y$ .

Simplify each term.

Apply the distributive property.

$5 \cdot 11 + 5 (2 y) - 8 y = 39$

$x = 11 + 2 y$

Multiply $5$ by $11$ .

$55 + 5 (2 y) - 8 y = 39$

$x = 11 + 2 y$

Multiply $2$ by $5$ .

$55 + 10 y - 8 y = 39$

$x = 11 + 2 y$

$55 + 10 y - 8 y = 39$

$x = 11 + 2 y$

Subtract $8 y$ from $10 y$ .

$55 + 2 y = 39$

$x = 11 + 2 y$

$55 + 2 y = 39$

$x = 11 + 2 y$

$55 + 2 y = 39$

$x = 11 + 2 y$

$55 + 2 y = 39$

$x = 11 + 2 y$

Solve for $y$ in $55 + 2 y = 39$ .

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

Subtract $55$ from both sides of the equation.

$2 y = 39 - 55$

$x = 11 + 2 y$

Subtract $55$ from $39$ .

$2 y = - 16$

$x = 11 + 2 y$

$2 y = - 16$

$x = 11 + 2 y$

Divide each term in $2 y = - 16$ by $2$ and simplify.

Divide each term in $2 y = - 16$ by $2$ .

$\frac{2 y}{2} = \frac{- 16}{2}$

$x = 11 + 2 y$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 16}{2}$

$x = 11 + 2 y$

Divide $y$ by $1$ .

$y = \frac{- 16}{2}$

$x = 11 + 2 y$

$y = \frac{- 16}{2}$

$x = 11 + 2 y$

$y = \frac{- 16}{2}$

$x = 11 + 2 y$

Simplify the right side.

Divide $- 16$ by $2$ .

$y = - 8$

$x = 11 + 2 y$

$y = - 8$

$x = 11 + 2 y$

$y = - 8$

$x = 11 + 2 y$

$y = - 8$

$x = 11 + 2 y$

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

Replace all occurrences of $y$ in $x = 11 + 2 y$ with $- 8$ .

$x = 11 + 2 (- 8)$

$y = - 8$

Simplify the right side.

Simplify $11 + 2 (- 8)$ .

Multiply $2$ by $- 8$ .

$x = 11 - 16$

$y = - 8$

Subtract $16$ from $11$ .

$x = - 5$

$y = - 8$

$x = - 5$

$y = - 8$

$x = - 5$

$y = - 8$

$x = - 5$

$y = - 8$

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

$(- 5, - 8)$

The result can be shown in multiple forms.

Point Form:

$(- 5, - 8)$

Equation Form:

$x = - 5, y = - 8$

Solve the System of Equations -x+2y=-11 and 5x-8y=39

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