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

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

Step 1

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

$(- 1) \cdot (3 x + 5 y) = (- 1) (20)$

$- 2 x + 5 y = 20$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (3 x + 5 y)$ .

Apply the distributive property.

$- 1 (3 x) - 1 (5 y) = (- 1) (20)$

$- 2 x + 5 y = 20$

Multiply.

Multiply $3$ by $- 1$ .

$- 3 x - 1 (5 y) = (- 1) (20)$

$- 2 x + 5 y = 20$

Multiply $5$ by $- 1$ .

$- 3 x - 5 y = (- 1) (20)$

$- 2 x + 5 y = 20$

$- 3 x - 5 y = (- 1) (20)$

$- 2 x + 5 y = 20$

$- 3 x - 5 y = (- 1) (20)$

$- 2 x + 5 y = 20$

$- 3 x - 5 y = (- 1) (20)$

$- 2 x + 5 y = 20$

Simplify the right side.

Multiply $- 1$ by $20$ .

$- 3 x - 5 y = - 20$

$- 2 x + 5 y = 20$

$- 3 x - 5 y = - 20$

$- 2 x + 5 y = 20$

$- 3 x - 5 y = - 20$

$- 2 x + 5 y = 20$

Step 3

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

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

Step 4

Divide each term in $- 5 x = 0$ by $- 5$ and simplify.

Divide each term in $- 5 x = 0$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{0}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{0}{- 5}$

Divide $x$ by $1$ .

$x = \frac{0}{- 5}$

Simplify the right side.

Divide $0$ by $- 5$ .

$x = 0$

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 $y$ .

$- 3 \cdot 0 - 5 y = - 20$

Simplify $- 3 \cdot 0 - 5 y$ .

Multiply $- 3$ by $0$ .

$0 - 5 y = - 20$

Subtract $5 y$ from $0$ .

$- 5 y = - 20$

Divide each term in $- 5 y = - 20$ by $- 5$ and simplify.

Divide each term in $- 5 y = - 20$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 20}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 20}{- 5}$

Divide $y$ by $1$ .

$y = \frac{- 20}{- 5}$

Simplify the right side.

Divide $- 20$ by $- 5$ .

$y = 4$

Step 6

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

$(0, 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(0, 4)$

Equation Form:

$x = 0, y = 4$

Step 8

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

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