Solve by Addition/Elimination -6x+5y=-1 -8x+4y=12

$- 6 x + 5 y = - 1$ $- 8 x + 4 y = 12$

Step 1

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

$(- 4) \cdot (- 6 x + 5 y) = (- 4) (- 1)$

$(5) \cdot (- 8 x + 4 y) = (5) (12)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 4) \cdot (- 6 x + 5 y)$ .

Apply the distributive property.

$- 4 (- 6 x) - 4 (5 y) = (- 4) (- 1)$

$(5) \cdot (- 8 x + 4 y) = (5) (12)$

Multiply.

Multiply $- 6$ by $- 4$ .

$24 x - 4 (5 y) = (- 4) (- 1)$

$(5) \cdot (- 8 x + 4 y) = (5) (12)$

Multiply $5$ by $- 4$ .

$24 x - 20 y = (- 4) (- 1)$

$(5) \cdot (- 8 x + 4 y) = (5) (12)$

$24 x - 20 y = (- 4) (- 1)$

$(5) \cdot (- 8 x + 4 y) = (5) (12)$

$24 x - 20 y = (- 4) (- 1)$

$(5) \cdot (- 8 x + 4 y) = (5) (12)$

$24 x - 20 y = (- 4) (- 1)$

$(5) \cdot (- 8 x + 4 y) = (5) (12)$

Simplify the right side.

Multiply $- 4$ by $- 1$ .

$24 x - 20 y = 4$

$(5) \cdot (- 8 x + 4 y) = (5) (12)$

$24 x - 20 y = 4$

$(5) \cdot (- 8 x + 4 y) = (5) (12)$

Simplify the left side.

Simplify $(5) \cdot (- 8 x + 4 y)$ .

Apply the distributive property.

$24 x - 20 y = 4$

$5 (- 8 x) + 5 (4 y) = (5) (12)$

Multiply.

Multiply $- 8$ by $5$ .

$24 x - 20 y = 4$

$- 40 x + 5 (4 y) = (5) (12)$

Multiply $4$ by $5$ .

$24 x - 20 y = 4$

$- 40 x + 20 y = (5) (12)$

$24 x - 20 y = 4$

$- 40 x + 20 y = (5) (12)$

$24 x - 20 y = 4$

$- 40 x + 20 y = (5) (12)$

$24 x - 20 y = 4$

$- 40 x + 20 y = (5) (12)$

Simplify the right side.

Multiply $5$ by $12$ .

$24 x - 20 y = 4$

$- 40 x + 20 y = 60$

$24 x - 20 y = 4$

$- 40 x + 20 y = 60$

$24 x - 20 y = 4$

$- 40 x + 20 y = 60$

Step 3

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

		$2$	$4$	$x$	$-$	$2$	$0$	$y$	$=$		$4$
$+$	$-$	$4$	$0$	$x$	$+$	$2$	$0$	$y$	$=$	$6$	$0$
	$-$	$1$	$6$	$x$					$=$	$6$	$4$

Step 4

Divide each term in $- 16 x = 64$ by $- 16$ and simplify.

Divide each term in $- 16 x = 64$ by $- 16$ .

$\frac{- 16 x}{- 16} = \frac{64}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 x}{- 16} = \frac{64}{- 16}$

Divide $x$ by $1$ .

$x = \frac{64}{- 16}$

Simplify the right side.

Divide $64$ by $- 16$ .

$x = - 4$

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 $y$ .

$24 (- 4) - 20 y = 4$

Multiply $24$ by $- 4$ .

$- 96 - 20 y = 4$

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

Add $96$ to both sides of the equation.

$- 20 y = 4 + 96$

Add $4$ and $96$ .

$- 20 y = 100$

Divide each term in $- 20 y = 100$ by $- 20$ and simplify.

Divide each term in $- 20 y = 100$ by $- 20$ .

$\frac{- 20 y}{- 20} = \frac{100}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 y}{- 20} = \frac{100}{- 20}$

Divide $y$ by $1$ .

$y = \frac{100}{- 20}$

Simplify the right side.

Divide $100$ by $- 20$ .

$y = - 5$

Step 6

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

$(- 4, - 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 4, - 5)$

Equation Form:

$x = - 4, y = - 5$

Step 8

Solve by Addition/Elimination -6x+5y=-1 -8x+4y=12

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