Solve by Addition/Elimination 5x+4y=-4 3x+4y=12

$5 x + 4 y = - 4$ $3 x + 4 y = 12$

Step 1

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

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

$3 x + 4 y = 12$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (5 x + 4 y)$ .

Apply the distributive property.

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

$3 x + 4 y = 12$

Multiply.

Multiply $5$ by $- 1$ .

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

$3 x + 4 y = 12$

Multiply $4$ by $- 1$ .

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

$3 x + 4 y = 12$

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

$3 x + 4 y = 12$

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

$3 x + 4 y = 12$

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

$3 x + 4 y = 12$

Simplify the right side.

Multiply $- 1$ by $- 4$ .

$- 5 x - 4 y = 4$

$3 x + 4 y = 12$

$- 5 x - 4 y = 4$

$3 x + 4 y = 12$

$- 5 x - 4 y = 4$

$3 x + 4 y = 12$

Step 3

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

	$-$	$5$	$x$	$-$	$4$	$y$	$=$		$4$
$+$		$3$	$x$	$+$	$4$	$y$	$=$	$1$	$2$
	$-$	$2$	$x$				$=$	$1$	$6$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $16$ by $- 2$ .

$x = - 8$

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 $y$ .

$- 5 \cdot - 8 - 4 y = 4$

Multiply $- 5$ by $- 8$ .

$40 - 4 y = 4$

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

Subtract $40$ from both sides of the equation.

$- 4 y = 4 - 40$

Subtract $40$ from $4$ .

$- 4 y = - 36$

Divide each term in $- 4 y = - 36$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 36$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 36}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 36}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 36}{- 4}$

Simplify the right side.

Divide $- 36$ by $- 4$ .

$y = 9$

Step 6

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

$(- 8, 9)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 8, 9)$

Equation Form:

$x = - 8, y = 9$

Step 8

Solve by Addition/Elimination 5x+4y=-4 3x+4y=12

Related Questions

Support LCMGCF.com by disabling your adblocker.