Solve by Addition/Elimination 2x+5y=-4 , -2x+3y=20

$2 x + 5 y = - 4$ , $- 2 x + 3 y = 20$

Step 1

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

		$2$	$x$	$+$	$5$	$y$	$=$	$-$	$4$
$+$	$-$	$2$	$x$	$+$	$3$	$y$	$=$	$2$	$0$
					$8$	$y$	$=$	$1$	$6$

Step 2

Divide each term in $8 y = 16$ by $8$ and simplify.

Divide each term in $8 y = 16$ by $8$ .

$\frac{8 y}{8} = \frac{16}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{16}{8}$

Divide $y$ by $1$ .

$y = \frac{16}{8}$

Simplify the right side.

Divide $16$ by $8$ .

$y = 2$

Step 3

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 $x$ .

$2 x + 5 (2) = - 4$

Multiply $5$ by $2$ .

$2 x + 10 = - 4$

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

Subtract $10$ from both sides of the equation.

$2 x = - 4 - 10$

Subtract $10$ from $- 4$ .

$2 x = - 14$

Divide each term in $2 x = - 14$ by $2$ and simplify.

Divide each term in $2 x = - 14$ by $2$ .

$\frac{2 x}{2} = \frac{- 14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 14}{2}$

Divide $x$ by $1$ .

$x = \frac{- 14}{2}$

Simplify the right side.

Divide $- 14$ by $2$ .

$x = - 7$

Step 4

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

$(- 7, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 7, 2)$

Equation Form:

$x = - 7, y = 2$

Step 6

Solve by Addition/Elimination 2x+5y=-4 , -2x+3y=20

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