Solve by Addition/Elimination 5x+4y=-2 3x+4y=10

$5 x + 4 y = - 2$ $3 x + 4 y = 10$

Step 1

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

$(- 1) \cdot (5 x + 4 y) = (- 1) (- 2)$

$3 x + 4 y = 10$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 1 (5 x) - 1 (4 y) = (- 1) (- 2)$

$3 x + 4 y = 10$

Multiply.

Multiply $5$ by $- 1$ .

$- 5 x - 1 (4 y) = (- 1) (- 2)$

$3 x + 4 y = 10$

Multiply $4$ by $- 1$ .

$- 5 x - 4 y = (- 1) (- 2)$

$3 x + 4 y = 10$

$- 5 x - 4 y = (- 1) (- 2)$

$3 x + 4 y = 10$

$- 5 x - 4 y = (- 1) (- 2)$

$3 x + 4 y = 10$

$- 5 x - 4 y = (- 1) (- 2)$

$3 x + 4 y = 10$

Simplify the right side.

Multiply $- 1$ by $- 2$ .

$- 5 x - 4 y = 2$

$3 x + 4 y = 10$

$- 5 x - 4 y = 2$

$3 x + 4 y = 10$

$- 5 x - 4 y = 2$

$3 x + 4 y = 10$

Step 3

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

	$-$	$5$	$x$	$-$	$4$	$y$	$=$		$2$
$+$		$3$	$x$	$+$	$4$	$y$	$=$	$1$	$0$
	$-$	$2$	$x$				$=$	$1$	$2$

Step 4

Divide each term in $- 2 x = 12$ by $- 2$ and simplify.

Divide each term in $- 2 x = 12$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{12}{- 2}$

Divide $x$ by $1$ .

$x = \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$x = - 6$

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 $y$ .

$- 5 \cdot - 6 - 4 y = 2$

Multiply $- 5$ by $- 6$ .

$30 - 4 y = 2$

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

Subtract $30$ from both sides of the equation.

$- 4 y = 2 - 30$

Subtract $30$ from $2$ .

$- 4 y = - 28$

Divide each term in $- 4 y = - 28$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 28$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 28}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 28}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 28}{- 4}$

Simplify the right side.

Divide $- 28$ by $- 4$ .

$y = 7$

Step 6

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

$(- 6, 7)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 6, 7)$

Equation Form:

$x = - 6, y = 7$

Step 8

Solve by Addition/Elimination 5x+4y=-2 3x+4y=10

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