Solve by Addition/Elimination 2x+5y=-13 3x-4y=-8

$2 x + 5 y = - 13$ $3 x - 4 y = - 8$

Step 1

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

$(- 3) \cdot (2 x + 5 y) = (- 3) (- 13)$

$(2) \cdot (3 x - 4 y) = (2) (- 8)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (2 x + 5 y)$ .

Apply the distributive property.

$- 3 (2 x) - 3 (5 y) = (- 3) (- 13)$

$(2) \cdot (3 x - 4 y) = (2) (- 8)$

Multiply.

Multiply $2$ by $- 3$ .

$- 6 x - 3 (5 y) = (- 3) (- 13)$

$(2) \cdot (3 x - 4 y) = (2) (- 8)$

Multiply $5$ by $- 3$ .

$- 6 x - 15 y = (- 3) (- 13)$

$(2) \cdot (3 x - 4 y) = (2) (- 8)$

$- 6 x - 15 y = (- 3) (- 13)$

$(2) \cdot (3 x - 4 y) = (2) (- 8)$

$- 6 x - 15 y = (- 3) (- 13)$

$(2) \cdot (3 x - 4 y) = (2) (- 8)$

$- 6 x - 15 y = (- 3) (- 13)$

$(2) \cdot (3 x - 4 y) = (2) (- 8)$

Simplify the right side.

Multiply $- 3$ by $- 13$ .

$- 6 x - 15 y = 39$

$(2) \cdot (3 x - 4 y) = (2) (- 8)$

$- 6 x - 15 y = 39$

$(2) \cdot (3 x - 4 y) = (2) (- 8)$

Simplify the left side.

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

Apply the distributive property.

$- 6 x - 15 y = 39$

$2 (3 x) + 2 (- 4 y) = (2) (- 8)$

Multiply.

Multiply $3$ by $2$ .

$- 6 x - 15 y = 39$

$6 x + 2 (- 4 y) = (2) (- 8)$

Multiply $- 4$ by $2$ .

$- 6 x - 15 y = 39$

$6 x - 8 y = (2) (- 8)$

$- 6 x - 15 y = 39$

$6 x - 8 y = (2) (- 8)$

$- 6 x - 15 y = 39$

$6 x - 8 y = (2) (- 8)$

$- 6 x - 15 y = 39$

$6 x - 8 y = (2) (- 8)$

Simplify the right side.

Multiply $2$ by $- 8$ .

$- 6 x - 15 y = 39$

$6 x - 8 y = - 16$

$- 6 x - 15 y = 39$

$6 x - 8 y = - 16$

$- 6 x - 15 y = 39$

$6 x - 8 y = - 16$

Step 3

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

	$-$	$6$	$x$	$-$	$1$	$5$	$y$	$=$		$3$	$9$
$+$		$6$	$x$		$-$	$8$	$y$	$=$	$-$	$1$	$6$
				$-$	$2$	$3$	$y$	$=$		$2$	$3$

Step 4

Divide each term in $- 23 y = 23$ by $- 23$ and simplify.

Divide each term in $- 23 y = 23$ by $- 23$ .

$\frac{- 23 y}{- 23} = \frac{23}{- 23}$

Simplify the left side.

Cancel the common factor of $- 23$ .

Cancel the common factor.

$\frac{- 23 y}{- 23} = \frac{23}{- 23}$

Divide $y$ by $1$ .

$y = \frac{23}{- 23}$

Simplify the right side.

Divide $23$ by $- 23$ .

$y = - 1$

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 $x$ .

$- 6 x - 15 \cdot - 1 = 39$

Multiply $- 15$ by $- 1$ .

$- 6 x + 15 = 39$

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

Subtract $15$ from both sides of the equation.

$- 6 x = 39 - 15$

Subtract $15$ from $39$ .

$- 6 x = 24$

Divide each term in $- 6 x = 24$ by $- 6$ and simplify.

Divide each term in $- 6 x = 24$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{24}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{24}{- 6}$

Divide $x$ by $1$ .

$x = \frac{24}{- 6}$

Simplify the right side.

Divide $24$ by $- 6$ .

$x = - 4$

Step 6

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

$(- 4, - 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 4, - 1)$

Equation Form:

$x = - 4, y = - 1$

Step 8

Solve by Addition/Elimination 2x+5y=-13 3x-4y=-8

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