Solve by Addition/Elimination 5x-2y=-19 2x+3y=0

$5 x - 2 y = - 19$ $2 x + 3 y = 0$

Step 1

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

$(3) \cdot (5 x - 2 y) = (3) (- 19)$

$(2) \cdot (2 x + 3 y) = (2) (0)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$3 (5 x) + 3 (- 2 y) = (3) (- 19)$

$(2) \cdot (2 x + 3 y) = (2) (0)$

Multiply.

Multiply $5$ by $3$ .

$15 x + 3 (- 2 y) = (3) (- 19)$

$(2) \cdot (2 x + 3 y) = (2) (0)$

Multiply $- 2$ by $3$ .

$15 x - 6 y = (3) (- 19)$

$(2) \cdot (2 x + 3 y) = (2) (0)$

$15 x - 6 y = (3) (- 19)$

$(2) \cdot (2 x + 3 y) = (2) (0)$

$15 x - 6 y = (3) (- 19)$

$(2) \cdot (2 x + 3 y) = (2) (0)$

$15 x - 6 y = (3) (- 19)$

$(2) \cdot (2 x + 3 y) = (2) (0)$

Simplify the right side.

Multiply $3$ by $- 19$ .

$15 x - 6 y = - 57$

$(2) \cdot (2 x + 3 y) = (2) (0)$

$15 x - 6 y = - 57$

$(2) \cdot (2 x + 3 y) = (2) (0)$

Simplify the left side.

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

Apply the distributive property.

$15 x - 6 y = - 57$

$2 (2 x) + 2 (3 y) = (2) (0)$

Multiply.

Multiply $2$ by $2$ .

$15 x - 6 y = - 57$

$4 x + 2 (3 y) = (2) (0)$

Multiply $3$ by $2$ .

$15 x - 6 y = - 57$

$4 x + 6 y = (2) (0)$

$15 x - 6 y = - 57$

$4 x + 6 y = (2) (0)$

$15 x - 6 y = - 57$

$4 x + 6 y = (2) (0)$

$15 x - 6 y = - 57$

$4 x + 6 y = (2) (0)$

Simplify the right side.

Multiply $2$ by $0$ .

$15 x - 6 y = - 57$

$4 x + 6 y = 0$

$15 x - 6 y = - 57$

$4 x + 6 y = 0$

$15 x - 6 y = - 57$

$4 x + 6 y = 0$

Step 3

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

	$1$	$5$	$x$	$-$	$6$	$y$	$=$	$-$	$5$	$7$
$+$		$4$	$x$	$+$	$6$	$y$	$=$			$0$
	$1$	$9$	$x$				$=$	$-$	$5$	$7$

Step 4

Divide each term in $19 x = - 57$ by $19$ and simplify.

Divide each term in $19 x = - 57$ by $19$ .

$\frac{19 x}{19} = \frac{- 57}{19}$

Simplify the left side.

Cancel the common factor of $19$ .

Cancel the common factor.

$\frac{19 x}{19} = \frac{- 57}{19}$

Divide $x$ by $1$ .

$x = \frac{- 57}{19}$

Simplify the right side.

Divide $- 57$ by $19$ .

$x = - 3$

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 $y$ .

$15 (- 3) - 6 y = - 57$

Multiply $15$ by $- 3$ .

$- 45 - 6 y = - 57$

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

Add $45$ to both sides of the equation.

$- 6 y = - 57 + 45$

Add $- 57$ and $45$ .

$- 6 y = - 12$

Divide each term in $- 6 y = - 12$ by $- 6$ and simplify.

Divide each term in $- 6 y = - 12$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 12}{- 6}$

Divide $y$ by $1$ .

$y = \frac{- 12}{- 6}$

Simplify the right side.

Divide $- 12$ by $- 6$ .

$y = 2$

Step 6

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

$(- 3, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 3, 2)$

Equation Form:

$x = - 3, y = 2$

Step 8

Solve by Addition/Elimination 5x-2y=-19 2x+3y=0

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