Solve by Addition/Elimination 6x+4y=32 -6x+4y=8

$6 x + 4 y = 32$ $- 6 x + 4 y = 8$

Step 1

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

$(- 1) \cdot (6 x + 4 y) = (- 1) (32)$

$- 6 x + 4 y = 8$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (6 x + 4 y)$ .

Apply the distributive property.

$- 1 (6 x) - 1 (4 y) = (- 1) (32)$

$- 6 x + 4 y = 8$

Multiply.

Multiply $6$ by $- 1$ .

$- 6 x - 1 (4 y) = (- 1) (32)$

$- 6 x + 4 y = 8$

Multiply $4$ by $- 1$ .

$- 6 x - 4 y = (- 1) (32)$

$- 6 x + 4 y = 8$

$- 6 x - 4 y = (- 1) (32)$

$- 6 x + 4 y = 8$

$- 6 x - 4 y = (- 1) (32)$

$- 6 x + 4 y = 8$

$- 6 x - 4 y = (- 1) (32)$

$- 6 x + 4 y = 8$

Simplify the right side.

Multiply $- 1$ by $32$ .

$- 6 x - 4 y = - 32$

$- 6 x + 4 y = 8$

$- 6 x - 4 y = - 32$

$- 6 x + 4 y = 8$

$- 6 x - 4 y = - 32$

$- 6 x + 4 y = 8$

Step 3

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

		$-$	$6$	$x$	$-$	$4$	$y$	$=$	$-$	$3$	$2$
$+$		$-$	$6$	$x$	$+$	$4$	$y$	$=$			$8$
	$-$	$1$	$2$	$x$				$=$	$-$	$2$	$4$

Step 4

Divide each term in $- 12 x = - 24$ by $- 12$ and simplify.

Divide each term in $- 12 x = - 24$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{- 24}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{- 24}{- 12}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 12}$

Simplify the right side.

Divide $- 24$ by $- 12$ .

$x = 2$

Step 5

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

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

$- 6 \cdot 2 - 4 y = - 32$

Multiply $- 6$ by $2$ .

$- 12 - 4 y = - 32$

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

Add $12$ to both sides of the equation.

$- 4 y = - 32 + 12$

Add $- 32$ and $12$ .

$- 4 y = - 20$

Divide each term in $- 4 y = - 20$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 20$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 20}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 20}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 20}{- 4}$

Simplify the right side.

Divide $- 20$ by $- 4$ .

$y = 5$

Step 6

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

$(2, 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, 5)$

Equation Form:

$x = 2, y = 5$

Step 8

Solve by Addition/Elimination 6x+4y=32 -6x+4y=8

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