Solve by Addition/Elimination 3x-4y=26 2x+8y=-36

$3 x - 4 y = 26$ $2 x + 8 y = - 36$

Step 1

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

$(- 2) \cdot (3 x - 4 y) = (- 2) (26)$

$(3) \cdot (2 x + 8 y) = (3) (- 36)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (3 x - 4 y)$ .

Apply the distributive property.

$- 2 (3 x) - 2 (- 4 y) = (- 2) (26)$

$(3) \cdot (2 x + 8 y) = (3) (- 36)$

Multiply.

Multiply $3$ by $- 2$ .

$- 6 x - 2 (- 4 y) = (- 2) (26)$

$(3) \cdot (2 x + 8 y) = (3) (- 36)$

Multiply $- 4$ by $- 2$ .

$- 6 x + 8 y = (- 2) (26)$

$(3) \cdot (2 x + 8 y) = (3) (- 36)$

$- 6 x + 8 y = (- 2) (26)$

$(3) \cdot (2 x + 8 y) = (3) (- 36)$

$- 6 x + 8 y = (- 2) (26)$

$(3) \cdot (2 x + 8 y) = (3) (- 36)$

$- 6 x + 8 y = (- 2) (26)$

$(3) \cdot (2 x + 8 y) = (3) (- 36)$

Simplify the right side.

Multiply $- 2$ by $26$ .

$- 6 x + 8 y = - 52$

$(3) \cdot (2 x + 8 y) = (3) (- 36)$

$- 6 x + 8 y = - 52$

$(3) \cdot (2 x + 8 y) = (3) (- 36)$

Simplify the left side.

Simplify $(3) \cdot (2 x + 8 y)$ .

Apply the distributive property.

$- 6 x + 8 y = - 52$

$3 (2 x) + 3 (8 y) = (3) (- 36)$

Multiply.

Multiply $2$ by $3$ .

$- 6 x + 8 y = - 52$

$6 x + 3 (8 y) = (3) (- 36)$

Multiply $8$ by $3$ .

$- 6 x + 8 y = - 52$

$6 x + 24 y = (3) (- 36)$

$- 6 x + 8 y = - 52$

$6 x + 24 y = (3) (- 36)$

$- 6 x + 8 y = - 52$

$6 x + 24 y = (3) (- 36)$

$- 6 x + 8 y = - 52$

$6 x + 24 y = (3) (- 36)$

Simplify the right side.

Multiply $3$ by $- 36$ .

$- 6 x + 8 y = - 52$

$6 x + 24 y = - 108$

$- 6 x + 8 y = - 52$

$6 x + 24 y = - 108$

$- 6 x + 8 y = - 52$

$6 x + 24 y = - 108$

Step 3

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

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

Step 4

Divide each term in $32 y = - 160$ by $32$ and simplify.

Divide each term in $32 y = - 160$ by $32$ .

$\frac{32 y}{32} = \frac{- 160}{32}$

Simplify the left side.

Cancel the common factor of $32$ .

Cancel the common factor.

$\frac{32 y}{32} = \frac{- 160}{32}$

Divide $y$ by $1$ .

$y = \frac{- 160}{32}$

Simplify the right side.

Divide $- 160$ by $32$ .

$y = - 5$

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 $x$ .

$- 6 x + 8 (- 5) = - 52$

Multiply $8$ by $- 5$ .

$- 6 x - 40 = - 52$

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

Add $40$ to both sides of the equation.

$- 6 x = - 52 + 40$

Add $- 52$ and $40$ .

$- 6 x = - 12$

Divide each term in $- 6 x = - 12$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 12$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 12}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 6}$

Simplify the right side.

Divide $- 12$ by $- 6$ .

$x = 2$

Step 6

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

$(2, - 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, - 5)$

Equation Form:

$x = 2, y = - 5$

Step 8

Solve by Addition/Elimination 3x-4y=26 2x+8y=-36

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