Solve by Addition/Elimination 5x+4y=5 5x+8y=25

$5 x + 4 y = 5$ $5 x + 8 y = 25$

Step 1

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

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

$5 x + 8 y = 25$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$5 x + 8 y = 25$

Multiply.

Multiply $5$ by $- 1$ .

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

$5 x + 8 y = 25$

Multiply $4$ by $- 1$ .

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

$5 x + 8 y = 25$

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

$5 x + 8 y = 25$

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

$5 x + 8 y = 25$

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

$5 x + 8 y = 25$

Simplify the right side.

Multiply $- 1$ by $5$ .

$- 5 x - 4 y = - 5$

$5 x + 8 y = 25$

$- 5 x - 4 y = - 5$

$5 x + 8 y = 25$

$- 5 x - 4 y = - 5$

$5 x + 8 y = 25$

Step 3

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

	$-$	$5$	$x$	$-$	$4$	$y$	$=$	$-$	$5$
$+$		$5$	$x$	$+$	$8$	$y$	$=$	$2$	$5$
					$4$	$y$	$=$	$2$	$0$

Step 4

Divide each term in $4 y = 20$ by $4$ and simplify.

Divide each term in $4 y = 20$ by $4$ .

$\frac{4 y}{4} = \frac{20}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{20}{4}$

Divide $y$ by $1$ .

$y = \frac{20}{4}$

Simplify the right side.

Divide $20$ by $4$ .

$y = 5$

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 $x$ .

$- 5 x - 4 \cdot 5 = - 5$

Multiply $- 4$ by $5$ .

$- 5 x - 20 = - 5$

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

Add $20$ to both sides of the equation.

$- 5 x = - 5 + 20$

Add $- 5$ and $20$ .

$- 5 x = 15$

Divide each term in $- 5 x = 15$ by $- 5$ and simplify.

Divide each term in $- 5 x = 15$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{15}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{15}{- 5}$

Divide $x$ by $1$ .

$x = \frac{15}{- 5}$

Simplify the right side.

Divide $15$ by $- 5$ .

$x = - 3$

Step 6

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

$(- 3, 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 3, 5)$

Equation Form:

$x = - 3, y = 5$

Step 8

Solve by Addition/Elimination 5x+4y=5 5x+8y=25

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