Solve by Addition/Elimination 5x-4y=-10 , -4x+5y=8

$5 x - 4 y = - 10$ , $- 4 x + 5 y = 8$

Step 1

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

$(4) \cdot (5 x - 4 y) = (4) (- 10)$

$(5) \cdot (- 4 x + 5 y) = (5) (8)$

Step 2

Simplify.

Simplify the left side.

Simplify $(4) \cdot (5 x - 4 y)$ .

Apply the distributive property.

$4 (5 x) + 4 (- 4 y) = (4) (- 10)$

$(5) \cdot (- 4 x + 5 y) = (5) (8)$

Multiply.

Multiply $5$ by $4$ .

$20 x + 4 (- 4 y) = (4) (- 10)$

$(5) \cdot (- 4 x + 5 y) = (5) (8)$

Multiply $- 4$ by $4$ .

$20 x - 16 y = (4) (- 10)$

$(5) \cdot (- 4 x + 5 y) = (5) (8)$

$20 x - 16 y = (4) (- 10)$

$(5) \cdot (- 4 x + 5 y) = (5) (8)$

$20 x - 16 y = (4) (- 10)$

$(5) \cdot (- 4 x + 5 y) = (5) (8)$

$20 x - 16 y = (4) (- 10)$

$(5) \cdot (- 4 x + 5 y) = (5) (8)$

Simplify the right side.

Multiply $4$ by $- 10$ .

$20 x - 16 y = - 40$

$(5) \cdot (- 4 x + 5 y) = (5) (8)$

$20 x - 16 y = - 40$

$(5) \cdot (- 4 x + 5 y) = (5) (8)$

Simplify the left side.

Simplify $(5) \cdot (- 4 x + 5 y)$ .

Apply the distributive property.

$20 x - 16 y = - 40$

$5 (- 4 x) + 5 (5 y) = (5) (8)$

Multiply.

Multiply $- 4$ by $5$ .

$20 x - 16 y = - 40$

$- 20 x + 5 (5 y) = (5) (8)$

Multiply $5$ by $5$ .

$20 x - 16 y = - 40$

$- 20 x + 25 y = (5) (8)$

$20 x - 16 y = - 40$

$- 20 x + 25 y = (5) (8)$

$20 x - 16 y = - 40$

$- 20 x + 25 y = (5) (8)$

$20 x - 16 y = - 40$

$- 20 x + 25 y = (5) (8)$

Simplify the right side.

Multiply $5$ by $8$ .

$20 x - 16 y = - 40$

$- 20 x + 25 y = 40$

$20 x - 16 y = - 40$

$- 20 x + 25 y = 40$

$20 x - 16 y = - 40$

$- 20 x + 25 y = 40$

Step 3

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

		$2$	$0$	$x$	$-$	$1$	$6$	$y$	$=$	$-$	$4$	$0$
$+$	$-$	$2$	$0$	$x$	$+$	$2$	$5$	$y$	$=$		$4$	$0$
							$9$	$y$	$=$			$0$

Step 4

Divide each term in $9 y = 0$ by $9$ and simplify.

Divide each term in $9 y = 0$ by $9$ .

$\frac{9 y}{9} = \frac{0}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{0}{9}$

Divide $y$ by $1$ .

$y = \frac{0}{9}$

Simplify the right side.

Divide $0$ by $9$ .

$y = 0$

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 $x$ .

$20 x - 16 \cdot 0 = - 40$

Simplify $20 x - 16 \cdot 0$ .

Multiply $- 16$ by $0$ .

$20 x + 0 = - 40$

Add $20 x$ and $0$ .

$20 x = - 40$

Divide each term in $20 x = - 40$ by $20$ and simplify.

Divide each term in $20 x = - 40$ by $20$ .

$\frac{20 x}{20} = \frac{- 40}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 x}{20} = \frac{- 40}{20}$

Divide $x$ by $1$ .

$x = \frac{- 40}{20}$

Simplify the right side.

Divide $- 40$ by $20$ .

$x = - 2$

Step 6

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

$(- 2, 0)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 2, 0)$

Equation Form:

$x = - 2, y = 0$

Step 8

Solve by Addition/Elimination 5x-4y=-10 , -4x+5y=8

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