Solve by Addition/Elimination 5x+y=-12 , 7x-3y=-52

$5 x + y = - 12$ , $7 x - 3 y = - 52$

Step 1

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

$(3) \cdot (5 x + y) = (3) (- 12)$

$7 x - 3 y = - 52$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$3 (5 x) + 3 y = (3) (- 12)$

$7 x - 3 y = - 52$

Multiply $5$ by $3$ .

$15 x + 3 y = (3) (- 12)$

$7 x - 3 y = - 52$

$15 x + 3 y = (3) (- 12)$

$7 x - 3 y = - 52$

$15 x + 3 y = (3) (- 12)$

$7 x - 3 y = - 52$

Simplify the right side.

Multiply $3$ by $- 12$ .

$15 x + 3 y = - 36$

$7 x - 3 y = - 52$

$15 x + 3 y = - 36$

$7 x - 3 y = - 52$

$15 x + 3 y = - 36$

$7 x - 3 y = - 52$

Step 3

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

	$1$	$5$	$x$	$+$	$3$	$y$	$=$	$-$	$3$	$6$
$+$		$7$	$x$	$-$	$3$	$y$	$=$	$-$	$5$	$2$
	$2$	$2$	$x$				$=$	$-$	$8$	$8$

Step 4

Divide each term in $22 x = - 88$ by $22$ and simplify.

Divide each term in $22 x = - 88$ by $22$ .

$\frac{22 x}{22} = \frac{- 88}{22}$

Simplify the left side.

Cancel the common factor of $22$ .

Cancel the common factor.

$\frac{22 x}{22} = \frac{- 88}{22}$

Divide $x$ by $1$ .

$x = \frac{- 88}{22}$

Simplify the right side.

Divide $- 88$ by $22$ .

$x = - 4$

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 $y$ .

$15 (- 4) + 3 y = - 36$

Multiply $15$ by $- 4$ .

$- 60 + 3 y = - 36$

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

Add $60$ to both sides of the equation.

$3 y = - 36 + 60$

Add $- 36$ and $60$ .

$3 y = 24$

Divide each term in $3 y = 24$ by $3$ and simplify.

Divide each term in $3 y = 24$ by $3$ .

$\frac{3 y}{3} = \frac{24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{24}{3}$

Divide $y$ by $1$ .

$y = \frac{24}{3}$

Simplify the right side.

Divide $24$ by $3$ .

$y = 8$

Step 6

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

$(- 4, 8)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 4, 8)$

Equation Form:

$x = - 4, y = 8$

Step 8

Solve by Addition/Elimination 5x+y=-12 , 7x-3y=-52

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