Solve by Addition/Elimination x-y=120 x+y=150

$x - y = 120$ $x + y = 150$

Step 1

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

$x - y = 120$

$(- 1) \cdot (x + y) = (- 1) (150)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$x - y = 120$

$- 1 x - 1 y = (- 1) (150)$

Rewrite negatives.

Rewrite $- 1 x$ as $- x$ .

$x - y = 120$

$- x - 1 y = (- 1) (150)$

Rewrite $- 1 y$ as $- y$ .

$x - y = 120$

$- x - y = (- 1) (150)$

$x - y = 120$

$- x - y = (- 1) (150)$

$x - y = 120$

$- x - y = (- 1) (150)$

$x - y = 120$

$- x - y = (- 1) (150)$

Simplify the right side.

Multiply $- 1$ by $150$ .

$x - y = 120$

$- x - y = - 150$

$x - y = 120$

$- x - y = - 150$

$x - y = 120$

$- x - y = - 150$

Step 3

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

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

Step 4

Divide each term in $- 2 y = - 30$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 30$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 30}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 30}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- 30}{- 2}$

Simplify the right side.

Divide $- 30$ by $- 2$ .

$y = 15$

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 $x$ .

$x - (15) = 120$

Multiply $- 1$ by $15$ .

$x - 15 = 120$

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

Add $15$ to both sides of the equation.

$x = 120 + 15$

Add $120$ and $15$ .

$x = 135$

Step 6

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

$(135, 15)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(135, 15)$

Equation Form:

$x = 135, y = 15$

Step 8

Solve by Addition/Elimination x-y=120 x+y=150

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