Solve for y 2x+3y=5x-y

$2 x + 3 y = 5 x - y$

Move all terms containing $y$ to the left side of the equation.

Add $y$ to both sides of the equation.

$2 x + 3 y + y = 5 x$

Add $3 y$ and $y$ .

$2 x + 4 y = 5 x$

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

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

$4 y = 5 x - 2 x$

Subtract $2 x$ from $5 x$ .

$4 y = 3 x$

Divide each term in $4 y = 3 x$ by $4$ and simplify.

Divide each term in $4 y = 3 x$ by $4$ .

$\frac{4 y}{4} = \frac{3 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{3 x}{4}$

Divide $y$ by $1$ .

$y = \frac{3 x}{4}$