Solve for y 3x+7y=x

$3 x + 7 y = x$

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

Subtract $3 x$ from both sides of the equation.

$7 y = x - 3 x$

Subtract $3 x$ from $x$ .

$7 y = - 2 x$

Divide each term in $7 y = - 2 x$ by $7$ and simplify.

Divide each term in $7 y = - 2 x$ by $7$ .

$\frac{7 y}{7} = \frac{- 2 x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 2 x}{7}$

Divide $y$ by $1$ .

$y = \frac{- 2 x}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{2 x}{7}$