Solve by Addition/Elimination -5y-10x=45 -3y+10x=-5

$- 5 y - 10 x = 45$ $- 3 y + 10 x = - 5$

Step 1

Simplify the left side.

Reorder $- 5 y$ and $- 10 x$ .

$- 10 x - 5 y = 45$

$- 3 y + 10 x = - 5$

$- 10 x - 5 y = 45$

$- 3 y + 10 x = - 5$

Step 2

Simplify the left side.

Reorder $- 3 y$ and $10 x$ .

$10 x - 3 y = - 5$

$- 10 x - 5 y = 45$

$10 x - 3 y = - 5$

$- 10 x - 5 y = 45$

Step 3

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

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

Step 4

Divide each term in $- 8 y = 40$ by $- 8$ and simplify.

Divide each term in $- 8 y = 40$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{40}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{40}{- 8}$

Divide $y$ by $1$ .

$y = \frac{40}{- 8}$

Simplify the right side.

Divide $40$ by $- 8$ .

$y = - 5$

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 $x$ .

$- 10 x - 5 \cdot - 5 = 45$

Multiply $- 5$ by $- 5$ .

$- 10 x + 25 = 45$

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

Subtract $25$ from both sides of the equation.

$- 10 x = 45 - 25$

Subtract $25$ from $45$ .

$- 10 x = 20$

Divide each term in $- 10 x = 20$ by $- 10$ and simplify.

Divide each term in $- 10 x = 20$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{20}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{20}{- 10}$

Divide $x$ by $1$ .

$x = \frac{20}{- 10}$

Simplify the right side.

Divide $20$ by $- 10$ .

$x = - 2$

Step 6

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

$(- 2, - 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 2, - 5)$

Equation Form:

$x = - 2, y = - 5$

Step 8

Solve by Addition/Elimination -5y-10x=45 -3y+10x=-5

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