Solve by Addition/Elimination 2x-3y=-22 8x+5y=14

$2 x - 3 y = - 22$ $8 x + 5 y = 14$

Step 1

Multiply each equation by the value that makes the coefficients of $x$ opposite.

$(- 4) \cdot (2 x - 3 y) = (- 4) (- 22)$

$8 x + 5 y = 14$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 4) \cdot (2 x - 3 y)$ .

Apply the distributive property.

$- 4 (2 x) - 4 (- 3 y) = (- 4) (- 22)$

$8 x + 5 y = 14$

Multiply.

Multiply $2$ by $- 4$ .

$- 8 x - 4 (- 3 y) = (- 4) (- 22)$

$8 x + 5 y = 14$

Multiply $- 3$ by $- 4$ .

$- 8 x + 12 y = (- 4) (- 22)$

$8 x + 5 y = 14$

$- 8 x + 12 y = (- 4) (- 22)$

$8 x + 5 y = 14$

$- 8 x + 12 y = (- 4) (- 22)$

$8 x + 5 y = 14$

$- 8 x + 12 y = (- 4) (- 22)$

$8 x + 5 y = 14$

Simplify the right side.

Multiply $- 4$ by $- 22$ .

$- 8 x + 12 y = 88$

$8 x + 5 y = 14$

$- 8 x + 12 y = 88$

$8 x + 5 y = 14$

$- 8 x + 12 y = 88$

$8 x + 5 y = 14$

Step 3

Add the two equations together to eliminate $x$ from the system.

	$-$	$8$	$x$	$+$	$1$	$2$	$y$	$=$	$8$	$8$
$+$		$8$	$x$	$+$		$5$	$y$	$=$	$1$	$4$
					$1$	$7$	$y$	$=$	$1$	$0$	$2$

Step 4

Divide each term in $17 y = 102$ by $17$ and simplify.

Divide each term in $17 y = 102$ by $17$ .

$\frac{17 y}{17} = \frac{102}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 y}{17} = \frac{102}{17}$

Divide $y$ by $1$ .

$y = \frac{102}{17}$

Simplify the right side.

Divide $102$ by $17$ .

$y = 6$

Step 5

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$- 8 x + 12 (6) = 88$

Multiply $12$ by $6$ .

$- 8 x + 72 = 88$

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

Subtract $72$ from both sides of the equation.

$- 8 x = 88 - 72$

Subtract $72$ from $88$ .

$- 8 x = 16$

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

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

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

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $16$ by $- 8$ .

$x = - 2$

Step 6

The solution to the independent system of equations can be represented as a point.

$(- 2, 6)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 2, 6)$

Equation Form:

$x = - 2, y = 6$

Step 8

Solve by Addition/Elimination 2x-3y=-22 8x+5y=14

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