Solve by Addition/Elimination 5x+4y=73 -4x+4y=-8

$5 x + 4 y = 73$ $- 4 x + 4 y = - 8$

Step 1

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

$(- 1) \cdot (5 x + 4 y) = (- 1) (73)$

$- 4 x + 4 y = - 8$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (5 x + 4 y)$ .

Apply the distributive property.

$- 1 (5 x) - 1 (4 y) = (- 1) (73)$

$- 4 x + 4 y = - 8$

Multiply.

Multiply $5$ by $- 1$ .

$- 5 x - 1 (4 y) = (- 1) (73)$

$- 4 x + 4 y = - 8$

Multiply $4$ by $- 1$ .

$- 5 x - 4 y = (- 1) (73)$

$- 4 x + 4 y = - 8$

$- 5 x - 4 y = (- 1) (73)$

$- 4 x + 4 y = - 8$

$- 5 x - 4 y = (- 1) (73)$

$- 4 x + 4 y = - 8$

$- 5 x - 4 y = (- 1) (73)$

$- 4 x + 4 y = - 8$

Simplify the right side.

Multiply $- 1$ by $73$ .

$- 5 x - 4 y = - 73$

$- 4 x + 4 y = - 8$

$- 5 x - 4 y = - 73$

$- 4 x + 4 y = - 8$

$- 5 x - 4 y = - 73$

$- 4 x + 4 y = - 8$

Step 3

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

	$-$	$5$	$x$	$-$	$4$	$y$	$=$	$-$	$7$	$3$
$+$	$-$	$4$	$x$	$+$	$4$	$y$	$=$		$-$	$8$
	$-$	$9$	$x$				$=$	$-$	$8$	$1$

Step 4

Divide each term in $- 9 x = - 81$ by $- 9$ and simplify.

Divide each term in $- 9 x = - 81$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{- 81}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{- 81}{- 9}$

Divide $x$ by $1$ .

$x = \frac{- 81}{- 9}$

Simplify the right side.

Divide $- 81$ by $- 9$ .

$x = 9$

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 $y$ .

$- 5 \cdot 9 - 4 y = - 73$

Multiply $- 5$ by $9$ .

$- 45 - 4 y = - 73$

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

Add $45$ to both sides of the equation.

$- 4 y = - 73 + 45$

Add $- 73$ and $45$ .

$- 4 y = - 28$

Divide each term in $- 4 y = - 28$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 28$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 28}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 28}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 28}{- 4}$

Simplify the right side.

Divide $- 28$ by $- 4$ .

$y = 7$

Step 6

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

$(9, 7)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(9, 7)$

Equation Form:

$x = 9, y = 7$

Step 8

Solve by Addition/Elimination 5x+4y=73 -4x+4y=-8

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