Solve by Graphing x-y=25 , 2x+3y=180

$x - y = 25$ , $2 x + 3 y = 180$

Step 1

Subtract $x$ from both sides of the equation.

$- y = 25 - x$

$2 x + 3 y = 180$

Step 2

Divide each term in $- y = 25 - x$ by $- 1$ and simplify.

Divide each term in $- y = 25 - x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{25}{- 1} + \frac{- x}{- 1}$

$2 x + 3 y = 180$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{25}{- 1} + \frac{- x}{- 1}$

$2 x + 3 y = 180$

Divide $y$ by $1$ .

$y = \frac{25}{- 1} + \frac{- x}{- 1}$

$2 x + 3 y = 180$

$y = \frac{25}{- 1} + \frac{- x}{- 1}$

$2 x + 3 y = 180$

Simplify the right side.

Simplify each term.

Divide $25$ by $- 1$ .

$y = - 25 + \frac{- x}{- 1}$

$2 x + 3 y = 180$

Dividing two negative values results in a positive value.

$y = - 25 + \frac{x}{1}$

$2 x + 3 y = 180$

Divide $x$ by $1$ .

$y = - 25 + x$

$2 x + 3 y = 180$

$y = - 25 + x$

$2 x + 3 y = 180$

$y = - 25 + x$

$2 x + 3 y = 180$

$y = - 25 + x$

$2 x + 3 y = 180$

Step 3

Subtract $2 x$ from both sides of the equation.

$3 y = 180 - 2 x$

$y = - 25 + x$

Step 4

Divide each term in $3 y = 180 - 2 x$ by $3$ and simplify.

Divide each term in $3 y = 180 - 2 x$ by $3$ .

$\frac{3 y}{3} = \frac{180}{3} + \frac{- 2 x}{3}$

$y = - 25 + x$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{180}{3} + \frac{- 2 x}{3}$

$y = - 25 + x$

Divide $y$ by $1$ .

$y = \frac{180}{3} + \frac{- 2 x}{3}$

$y = - 25 + x$

$y = \frac{180}{3} + \frac{- 2 x}{3}$

$y = - 25 + x$

$y = \frac{180}{3} + \frac{- 2 x}{3}$

$y = - 25 + x$

Simplify the right side.

Simplify each term.

Divide $180$ by $3$ .

$y = 60 + \frac{- 2 x}{3}$

$y = - 25 + x$

Move the negative in front of the fraction.

$y = 60 - \frac{2 x}{3}$

$y = - 25 + x$

$y = 60 - \frac{2 x}{3}$

$y = - 25 + x$

$y = 60 - \frac{2 x}{3}$

$y = - 25 + x$

$y = 60 - \frac{2 x}{3}$

$y = - 25 + x$

Step 5

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(51, 26)$

Step 6

Solve by Graphing x-y=25 , 2x+3y=180

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