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

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

Step 1

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

Add $7 y$ to both sides of the equation.

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

Subtract $35$ from both sides of the equation.

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

Step 2

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

Factor $x$ out of $x y$ .

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

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

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

Factor $x$ out of $x (y) + x \cdot - 5$ .

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

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $y - 5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Combine the numerators over the common denominator.

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

Factor $7$ out of $7 y - 35$ .

Factor $7$ out of $7 y$ .

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

Factor $7$ out of $- 35$ .

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

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

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

Cancel the common factor of $y - 5$ .

Cancel the common factor.

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

Divide $7$ by $1$ .

$x = 7$