Solve by Substitution x-y=120 , x+y=150

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

Step 1

Add $y$ to both sides of the equation.

$x = 120 + y$

$x + y = 150$

Step 2

Replace all occurrences of $x$ with $120 + y$ in each equation.

Replace all occurrences of $x$ in $x + y = 150$ with $120 + y$ .

$(120 + y) + y = 150$

$x = 120 + y$

Simplify the left side.

Add $y$ and $y$ .

$120 + 2 y = 150$

$x = 120 + y$

$120 + 2 y = 150$

$x = 120 + y$

$120 + 2 y = 150$

$x = 120 + y$

Step 3

Solve for $y$ in $120 + 2 y = 150$ .

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

Subtract $120$ from both sides of the equation.

$2 y = 150 - 120$

$x = 120 + y$

Subtract $120$ from $150$ .

$2 y = 30$

$x = 120 + y$

$2 y = 30$

$x = 120 + y$

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

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

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

$x = 120 + y$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$x = 120 + y$

Divide $y$ by $1$ .

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

$x = 120 + y$

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

$x = 120 + y$

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

$x = 120 + y$

Simplify the right side.

Divide $30$ by $2$ .

$y = 15$

$x = 120 + y$

$y = 15$

$x = 120 + y$

$y = 15$

$x = 120 + y$

$y = 15$

$x = 120 + y$

Step 4

Replace all occurrences of $y$ with $15$ in each equation.

Replace all occurrences of $y$ in $x = 120 + y$ with $15$ .

$x = 120 + 15$

$y = 15$

Simplify $x = 120 + 15$ .

Simplify the left side.

Remove parentheses.

$x = 120 + 15$

$y = 15$

$x = 120 + 15$

$y = 15$

Simplify the right side.

Add $120$ and $15$ .

$x = 135$

$y = 15$

$x = 135$

$y = 15$

$x = 135$

$y = 15$

$x = 135$

$y = 15$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(135, 15)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(135, 15)$

Equation Form:

$x = 135, y = 15$

Step 7

Solve by Substitution x-y=120 , x+y=150

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