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

$3 x - 4 y = - 20$ $3 x - 2 y = - 4$

Step 1

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

$(- 1) \cdot (3 x - 4 y) = (- 1) (- 20)$

$3 x - 2 y = - 4$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (3 x - 4 y)$ .

Apply the distributive property.

$- 1 (3 x) - 1 (- 4 y) = (- 1) (- 20)$

$3 x - 2 y = - 4$

Multiply.

Multiply $3$ by $- 1$ .

$- 3 x - 1 (- 4 y) = (- 1) (- 20)$

$3 x - 2 y = - 4$

Multiply $- 4$ by $- 1$ .

$- 3 x + 4 y = (- 1) (- 20)$

$3 x - 2 y = - 4$

$- 3 x + 4 y = (- 1) (- 20)$

$3 x - 2 y = - 4$

$- 3 x + 4 y = (- 1) (- 20)$

$3 x - 2 y = - 4$

$- 3 x + 4 y = (- 1) (- 20)$

$3 x - 2 y = - 4$

Simplify the right side.

Multiply $- 1$ by $- 20$ .

$- 3 x + 4 y = 20$

$3 x - 2 y = - 4$

$- 3 x + 4 y = 20$

$3 x - 2 y = - 4$

$- 3 x + 4 y = 20$

$3 x - 2 y = - 4$

Step 3

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

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

Step 4

Divide each term in $2 y = 16$ by $2$ and simplify.

Divide each term in $2 y = 16$ by $2$ .

$\frac{2 y}{2} = \frac{16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{16}{2}$

Divide $y$ by $1$ .

$y = \frac{16}{2}$

Simplify the right side.

Divide $16$ by $2$ .

$y = 8$

Step 5

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 $x$ .

$- 3 x + 4 (8) = 20$

Multiply $4$ by $8$ .

$- 3 x + 32 = 20$

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

Subtract $32$ from both sides of the equation.

$- 3 x = 20 - 32$

Subtract $32$ from $20$ .

$- 3 x = - 12$

Divide each term in $- 3 x = - 12$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 12$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 12}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 3}$

Simplify the right side.

Divide $- 12$ by $- 3$ .

$x = 4$

Step 6

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

$(4, 8)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, 8)$

Equation Form:

$x = 4, y = 8$

Step 8

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

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