Find the Points of Intersection x-y=25 , 2x+3y=180

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

Step 1

Add $y$ to both sides of the equation.

$x = 25 + y$

$2 x + 3 y = 180$

Step 2

Replace all occurrences of $x$ with $25 + y$ in each equation.

Replace all occurrences of $x$ in $2 x + 3 y = 180$ with $25 + y$ .

$2 (25 + y) + 3 y = 180$

$x = 25 + y$

Simplify the left side.

Simplify $2 (25 + y) + 3 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 25 + 2 y + 3 y = 180$

$x = 25 + y$

Multiply $2$ by $25$ .

$50 + 2 y + 3 y = 180$

$x = 25 + y$

$50 + 2 y + 3 y = 180$

$x = 25 + y$

Add $2 y$ and $3 y$ .

$50 + 5 y = 180$

$x = 25 + y$

$50 + 5 y = 180$

$x = 25 + y$

$50 + 5 y = 180$

$x = 25 + y$

$50 + 5 y = 180$

$x = 25 + y$

Step 3

Solve for $y$ in $50 + 5 y = 180$ .

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

Subtract $50$ from both sides of the equation.

$5 y = 180 - 50$

$x = 25 + y$

Subtract $50$ from $180$ .

$5 y = 130$

$x = 25 + y$

$5 y = 130$

$x = 25 + y$

Divide each term in $5 y = 130$ by $5$ and simplify.

Divide each term in $5 y = 130$ by $5$ .

$\frac{5 y}{5} = \frac{130}{5}$

$x = 25 + y$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{130}{5}$

$x = 25 + y$

Divide $y$ by $1$ .

$y = \frac{130}{5}$

$x = 25 + y$

$y = \frac{130}{5}$

$x = 25 + y$

$y = \frac{130}{5}$

$x = 25 + y$

Simplify the right side.

Divide $130$ by $5$ .

$y = 26$

$x = 25 + y$

$y = 26$

$x = 25 + y$

$y = 26$

$x = 25 + y$

$y = 26$

$x = 25 + y$

Step 4

Replace all occurrences of $y$ with $26$ in each equation.

Replace all occurrences of $y$ in $x = 25 + y$ with $26$ .

$x = 25 + 26$

$y = 26$

Simplify $x = 25 + 26$ .

Simplify the left side.

Remove parentheses.

$x = 25 + 26$

$y = 26$

$x = 25 + 26$

$y = 26$

Simplify the right side.

Add $25$ and $26$ .

$x = 51$

$y = 26$

$x = 51$

$y = 26$

$x = 51$

$y = 26$

$x = 51$

$y = 26$

Step 5

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

$(51, 26)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(51, 26)$

Equation Form:

$x = 51, y = 26$

Step 7

Find the Points of Intersection x-y=25 , 2x+3y=180

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