Solve by Addition/Elimination 2x-3y=4 5x+2y=-9

$2 x - 3 y = 4$ $5 x + 2 y = - 9$

Step 1

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

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

$(3) \cdot (5 x + 2 y) = (3) (- 9)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$(3) \cdot (5 x + 2 y) = (3) (- 9)$

Multiply.

Multiply $2$ by $2$ .

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

$(3) \cdot (5 x + 2 y) = (3) (- 9)$

Multiply $- 3$ by $2$ .

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

$(3) \cdot (5 x + 2 y) = (3) (- 9)$

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

$(3) \cdot (5 x + 2 y) = (3) (- 9)$

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

$(3) \cdot (5 x + 2 y) = (3) (- 9)$

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

$(3) \cdot (5 x + 2 y) = (3) (- 9)$

Simplify the right side.

Multiply $2$ by $4$ .

$4 x - 6 y = 8$

$(3) \cdot (5 x + 2 y) = (3) (- 9)$

$4 x - 6 y = 8$

$(3) \cdot (5 x + 2 y) = (3) (- 9)$

Simplify the left side.

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

Apply the distributive property.

$4 x - 6 y = 8$

$3 (5 x) + 3 (2 y) = (3) (- 9)$

Multiply.

Multiply $5$ by $3$ .

$4 x - 6 y = 8$

$15 x + 3 (2 y) = (3) (- 9)$

Multiply $2$ by $3$ .

$4 x - 6 y = 8$

$15 x + 6 y = (3) (- 9)$

$4 x - 6 y = 8$

$15 x + 6 y = (3) (- 9)$

$4 x - 6 y = 8$

$15 x + 6 y = (3) (- 9)$

$4 x - 6 y = 8$

$15 x + 6 y = (3) (- 9)$

Simplify the right side.

Multiply $3$ by $- 9$ .

$4 x - 6 y = 8$

$15 x + 6 y = - 27$

$4 x - 6 y = 8$

$15 x + 6 y = - 27$

$4 x - 6 y = 8$

$15 x + 6 y = - 27$

Step 3

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

		$4$	$x$	$-$	$6$	$y$	$=$			$8$
$+$	$1$	$5$	$x$	$+$	$6$	$y$	$=$	$-$	$2$	$7$
	$1$	$9$	$x$				$=$	$-$	$1$	$9$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $19$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 19$ by $19$ .

$x = - 1$

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 $y$ .

$4 (- 1) - 6 y = 8$

Multiply $4$ by $- 1$ .

$- 4 - 6 y = 8$

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

Add $4$ to both sides of the equation.

$- 6 y = 8 + 4$

Add $8$ and $4$ .

$- 6 y = 12$

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.

$(- 1, - 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 1, - 2)$

Equation Form:

$x = - 1, y = - 2$

Step 8

Solve by Addition/Elimination 2x-3y=4 5x+2y=-9

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