Solve by Addition/Elimination -5y+8x=-18 5y+2x=58

$- 5 y + 8 x = - 18$ $5 y + 2 x = 58$

Step 1

Simplify the left side.

Reorder $- 5 y$ and $8 x$ .

$8 x - 5 y = - 18$

$5 y + 2 x = 58$

$8 x - 5 y = - 18$

$5 y + 2 x = 58$

Step 2

Simplify the left side.

Reorder $5 y$ and $2 x$ .

$2 x + 5 y = 58$

$8 x - 5 y = - 18$

$2 x + 5 y = 58$

$8 x - 5 y = - 18$

Step 3

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

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

Step 4

Divide each term in $10 x = 40$ by $10$ and simplify.

Divide each term in $10 x = 40$ by $10$ .

$\frac{10 x}{10} = \frac{40}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{40}{10}$

Divide $x$ by $1$ .

$x = \frac{40}{10}$

Simplify the right side.

Divide $40$ by $10$ .

$x = 4$

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 $y$ .

$8 (4) - 5 y = - 18$

Multiply $8$ by $4$ .

$32 - 5 y = - 18$

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

Subtract $32$ from both sides of the equation.

$- 5 y = - 18 - 32$

Subtract $32$ from $- 18$ .

$- 5 y = - 50$

Divide each term in $- 5 y = - 50$ by $- 5$ and simplify.

Divide each term in $- 5 y = - 50$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 50}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 50}{- 5}$

Divide $y$ by $1$ .

$y = \frac{- 50}{- 5}$

Simplify the right side.

Divide $- 50$ by $- 5$ .

$y = 10$

Step 6

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

$(4, 10)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, 10)$

Equation Form:

$x = 4, y = 10$

Step 8

Solve by Addition/Elimination -5y+8x=-18 5y+2x=58

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