Solve the System of Equations 8x+y=-13 -8x-2y=10

$8 x + y = - 13$ $- 8 x - 2 y = 10$

Step 1

Subtract $8 x$ from both sides of the equation.

$y = - 13 - 8 x$

$- 8 x - 2 y = 10$

Step 2

Replace all occurrences of $y$ with $- 13 - 8 x$ in each equation.

Replace all occurrences of $y$ in $- 8 x - 2 y = 10$ with $- 13 - 8 x$ .

$- 8 x - 2 (- 13 - 8 x) = 10$

$y = - 13 - 8 x$

Simplify the left side.

Simplify $- 8 x - 2 (- 13 - 8 x)$ .

Simplify each term.

Apply the distributive property.

$- 8 x - 2 \cdot - 13 - 2 (- 8 x) = 10$

$y = - 13 - 8 x$

Multiply $- 2$ by $- 13$ .

$- 8 x + 26 - 2 (- 8 x) = 10$

$y = - 13 - 8 x$

Multiply $- 8$ by $- 2$ .

$- 8 x + 26 + 16 x = 10$

$y = - 13 - 8 x$

$- 8 x + 26 + 16 x = 10$

$y = - 13 - 8 x$

Add $- 8 x$ and $16 x$ .

$8 x + 26 = 10$

$y = - 13 - 8 x$

$8 x + 26 = 10$

$y = - 13 - 8 x$

$8 x + 26 = 10$

$y = - 13 - 8 x$

$8 x + 26 = 10$

$y = - 13 - 8 x$

Step 3

Solve for $x$ in $8 x + 26 = 10$ .

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

Subtract $26$ from both sides of the equation.

$8 x = 10 - 26$

$y = - 13 - 8 x$

Subtract $26$ from $10$ .

$8 x = - 16$

$y = - 13 - 8 x$

$8 x = - 16$

$y = - 13 - 8 x$

Divide each term in $8 x = - 16$ by $8$ and simplify.

Divide each term in $8 x = - 16$ by $8$ .

$\frac{8 x}{8} = \frac{- 16}{8}$

$y = - 13 - 8 x$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 16}{8}$

$y = - 13 - 8 x$

Divide $x$ by $1$ .

$x = \frac{- 16}{8}$

$y = - 13 - 8 x$

$x = \frac{- 16}{8}$

$y = - 13 - 8 x$

$x = \frac{- 16}{8}$

$y = - 13 - 8 x$

Simplify the right side.

Divide $- 16$ by $8$ .

$x = - 2$

$y = - 13 - 8 x$

$x = - 2$

$y = - 13 - 8 x$

$x = - 2$

$y = - 13 - 8 x$

$x = - 2$

$y = - 13 - 8 x$

Step 4

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

Replace all occurrences of $x$ in $y = - 13 - 8 x$ with $- 2$ .

$y = - 13 - 8 \cdot - 2$

$x = - 2$

Simplify the right side.

Simplify $- 13 - 8 \cdot - 2$ .

Multiply $- 8$ by $- 2$ .

$y = - 13 + 16$

$x = - 2$

Add $- 13$ and $16$ .

$y = 3$

$x = - 2$

$y = 3$

$x = - 2$

$y = 3$

$x = - 2$

$y = 3$

$x = - 2$

Step 5

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

$(- 2, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, 3)$

Equation Form:

$x = - 2, y = 3$

Step 7

Solve the System of Equations 8x+y=-13 -8x-2y=10

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