Solve for y xy-5x-7y+35=0

$x y - 5 x - 7 y + 35 = 0$

Step 1

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

Add $5 x$ to both sides of the equation.

$x y - 7 y + 35 = 5 x$

Subtract $35$ from both sides of the equation.

$x y - 7 y = 5 x - 35$

Step 2

Factor $y$ out of $x y - 7 y$ .

Factor $y$ out of $x y$ .

$y x - 7 y = 5 x - 35$

Factor $y$ out of $- 7 y$ .

$y x + y \cdot - 7 = 5 x - 35$

Factor $y$ out of $y x + y \cdot - 7$ .

$y (x - 7) = 5 x - 35$

Step 3

Divide each term in $y (x - 7) = 5 x - 35$ by $x - 7$ and simplify.

Divide each term in $y (x - 7) = 5 x - 35$ by $x - 7$ .

$\frac{y (x - 7)}{x - 7} = \frac{5 x}{x - 7} + \frac{- 35}{x - 7}$

Simplify the left side.

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$\frac{y (x - 7)}{x - 7} = \frac{5 x}{x - 7} + \frac{- 35}{x - 7}$

Divide $y$ by $1$ .

$y = \frac{5 x}{x - 7} + \frac{- 35}{x - 7}$

Simplify the right side.

Combine the numerators over the common denominator.

$y = \frac{5 x - 35}{x - 7}$

Factor $5$ out of $5 x - 35$ .

Factor $5$ out of $5 x$ .

$y = \frac{5 (x) - 35}{x - 7}$

Factor $5$ out of $- 35$ .

$y = \frac{5 x + 5 \cdot - 7}{x - 7}$

Factor $5$ out of $5 x + 5 \cdot - 7$ .

$y = \frac{5 (x - 7)}{x - 7}$

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$y = \frac{5 (x - 7)}{x - 7}$

Divide $5$ by $1$ .

$y = 5$