Solve by Addition/Elimination 4x+5y=10 8x+5y=30

$4 x + 5 y = 10$ $8 x + 5 y = 30$

Step 1

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

$(- 1) \cdot (4 x + 5 y) = (- 1) (10)$

$8 x + 5 y = 30$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 1 (4 x) - 1 (5 y) = (- 1) (10)$

$8 x + 5 y = 30$

Multiply.

Multiply $4$ by $- 1$ .

$- 4 x - 1 (5 y) = (- 1) (10)$

$8 x + 5 y = 30$

Multiply $5$ by $- 1$ .

$- 4 x - 5 y = (- 1) (10)$

$8 x + 5 y = 30$

$- 4 x - 5 y = (- 1) (10)$

$8 x + 5 y = 30$

$- 4 x - 5 y = (- 1) (10)$

$8 x + 5 y = 30$

$- 4 x - 5 y = (- 1) (10)$

$8 x + 5 y = 30$

Simplify the right side.

Multiply $- 1$ by $10$ .

$- 4 x - 5 y = - 10$

$8 x + 5 y = 30$

$- 4 x - 5 y = - 10$

$8 x + 5 y = 30$

$- 4 x - 5 y = - 10$

$8 x + 5 y = 30$

Step 3

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

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

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $20$ by $4$ .

$x = 5$

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 $y$ .

$- 4 \cdot 5 - 5 y = - 10$

Multiply $- 4$ by $5$ .

$- 20 - 5 y = - 10$

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

Add $20$ to both sides of the equation.

$- 5 y = - 10 + 20$

Add $- 10$ and $20$ .

$- 5 y = 10$

Divide each term in $- 5 y = 10$ by $- 5$ and simplify.

Divide each term in $- 5 y = 10$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{10}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{10}{- 5}$

Divide $y$ by $1$ .

$y = \frac{10}{- 5}$

Simplify the right side.

Divide $10$ by $- 5$ .

$y = - 2$

Step 6

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

$(5, - 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(5, - 2)$

Equation Form:

$x = 5, y = - 2$

Step 8

Solve by Addition/Elimination 4x+5y=10 8x+5y=30

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