Solve by Addition/Elimination 2x-5y=2 3x+2y=-16

$2 x - 5 y = 2$ $3 x + 2 y = - 16$

Step 1

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

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

$(2) \cdot (3 x + 2 y) = (2) (- 16)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$(2) \cdot (3 x + 2 y) = (2) (- 16)$

Multiply.

Multiply $2$ by $- 3$ .

$- 6 x - 3 (- 5 y) = (- 3) (2)$

$(2) \cdot (3 x + 2 y) = (2) (- 16)$

Multiply $- 5$ by $- 3$ .

$- 6 x + 15 y = (- 3) (2)$

$(2) \cdot (3 x + 2 y) = (2) (- 16)$

$- 6 x + 15 y = (- 3) (2)$

$(2) \cdot (3 x + 2 y) = (2) (- 16)$

$- 6 x + 15 y = (- 3) (2)$

$(2) \cdot (3 x + 2 y) = (2) (- 16)$

$- 6 x + 15 y = (- 3) (2)$

$(2) \cdot (3 x + 2 y) = (2) (- 16)$

Simplify the right side.

Multiply $- 3$ by $2$ .

$- 6 x + 15 y = - 6$

$(2) \cdot (3 x + 2 y) = (2) (- 16)$

$- 6 x + 15 y = - 6$

$(2) \cdot (3 x + 2 y) = (2) (- 16)$

Simplify the left side.

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

Apply the distributive property.

$- 6 x + 15 y = - 6$

$2 (3 x) + 2 (2 y) = (2) (- 16)$

Multiply.

Multiply $3$ by $2$ .

$- 6 x + 15 y = - 6$

$6 x + 2 (2 y) = (2) (- 16)$

Multiply $2$ by $2$ .

$- 6 x + 15 y = - 6$

$6 x + 4 y = (2) (- 16)$

$- 6 x + 15 y = - 6$

$6 x + 4 y = (2) (- 16)$

$- 6 x + 15 y = - 6$

$6 x + 4 y = (2) (- 16)$

$- 6 x + 15 y = - 6$

$6 x + 4 y = (2) (- 16)$

Simplify the right side.

Multiply $2$ by $- 16$ .

$- 6 x + 15 y = - 6$

$6 x + 4 y = - 32$

$- 6 x + 15 y = - 6$

$6 x + 4 y = - 32$

$- 6 x + 15 y = - 6$

$6 x + 4 y = - 32$

Step 3

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

	$-$	$6$	$x$	$+$	$1$	$5$	$y$	$=$		$-$	$6$
$+$		$6$	$x$	$+$		$4$	$y$	$=$	$-$	$3$	$2$
					$1$	$9$	$y$	$=$	$-$	$3$	$8$

Step 4

Divide each term in $19 y = - 38$ by $19$ and simplify.

Divide each term in $19 y = - 38$ by $19$ .

$\frac{19 y}{19} = \frac{- 38}{19}$

Simplify the left side.

Cancel the common factor of $19$ .

Cancel the common factor.

$\frac{19 y}{19} = \frac{- 38}{19}$

Divide $y$ by $1$ .

$y = \frac{- 38}{19}$

Simplify the right side.

Divide $- 38$ by $19$ .

$y = - 2$

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 $x$ .

$- 6 x + 15 (- 2) = - 6$

Multiply $15$ by $- 2$ .

$- 6 x - 30 = - 6$

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

Add $30$ to both sides of the equation.

$- 6 x = - 6 + 30$

Add $- 6$ and $30$ .

$- 6 x = 24$

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.

$(- 4, - 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 4, - 2)$

Equation Form:

$x = - 4, y = - 2$

Step 8

Solve by Addition/Elimination 2x-5y=2 3x+2y=-16

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