Solve by Addition/Elimination 2x-3y=-15 , x=4y

$2 x - 3 y = - 15$ , $x = 4 y$

Step 1

Subtract $4 y$ from both sides of the equation.

$2 x - 3 y = - 15, x - 4 y = 0$

Step 2

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

$2 x - 3 y = - 15$

$(- 2) \cdot (x - 4 y) = (- 2) (0)$

Step 3

Simplify.

Simplify the left side.

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

Apply the distributive property.

$2 x - 3 y = - 15$

$- 2 x - 2 (- 4 y) = (- 2) (0)$

Multiply $- 4$ by $- 2$ .

$2 x - 3 y = - 15$

$- 2 x + 8 y = (- 2) (0)$

$2 x - 3 y = - 15$

$- 2 x + 8 y = (- 2) (0)$

$2 x - 3 y = - 15$

$- 2 x + 8 y = (- 2) (0)$

Simplify the right side.

Multiply $- 2$ by $0$ .

$2 x - 3 y = - 15$

$- 2 x + 8 y = 0$

$2 x - 3 y = - 15$

$- 2 x + 8 y = 0$

$2 x - 3 y = - 15$

$- 2 x + 8 y = 0$

Step 4

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

		$2$	$x$	$-$	$3$	$y$	$=$	$-$	$1$	$5$
$+$	$-$	$2$	$x$	$+$	$8$	$y$	$=$			$0$
					$5$	$y$	$=$	$-$	$1$	$5$

Step 5

Divide each term in $5 y = - 15$ by $5$ and simplify.

Divide each term in $5 y = - 15$ by $5$ .

$\frac{5 y}{5} = \frac{- 15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 15}{5}$

Divide $y$ by $1$ .

$y = \frac{- 15}{5}$

Simplify the right side.

Divide $- 15$ by $5$ .

$y = - 3$

Step 6

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 $x$ .

$2 x - 3 \cdot - 3 = - 15$

Multiply $- 3$ by $- 3$ .

$2 x + 9 = - 15$

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

Subtract $9$ from both sides of the equation.

$2 x = - 15 - 9$

Subtract $9$ from $- 15$ .

$2 x = - 24$

Divide each term in $2 x = - 24$ by $2$ and simplify.

Divide each term in $2 x = - 24$ by $2$ .

$\frac{2 x}{2} = \frac{- 24}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 24}{2}$

Divide $x$ by $1$ .

$x = \frac{- 24}{2}$

Simplify the right side.

Divide $- 24$ by $2$ .

$x = - 12$

Step 7

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

$(- 12, - 3)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 12, - 3)$

Equation Form:

$x = - 12, y = - 3$

Step 9

Solve by Addition/Elimination 2x-3y=-15 , x=4y

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