Solve for y 6x+y=4x+11y

$6 x + y = 4 x + 11 y$

Step 1

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

Subtract $11 y$ from both sides of the equation.

$6 x + y - 11 y = 4 x$

Subtract $11 y$ from $y$ .

$6 x - 10 y = 4 x$

Step 2

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

Subtract $6 x$ from both sides of the equation.

$- 10 y = 4 x - 6 x$

Subtract $6 x$ from $4 x$ .

$- 10 y = - 2 x$

Step 3

Divide each term in $- 10 y = - 2 x$ by $- 10$ and simplify.

Divide each term in $- 10 y = - 2 x$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{- 2 x}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{- 2 x}{- 10}$

Divide $y$ by $1$ .

$y = \frac{- 2 x}{- 10}$

Simplify the right side.

Cancel the common factor of $- 2$ and $- 10$ .

Factor $- 2$ out of $- 2 x$ .

$y = \frac{- 2 (x)}{- 10}$

Cancel the common factors.

Factor $- 2$ out of $- 10$ .

$y = \frac{- 2 (x)}{- 2 (5)}$

Cancel the common factor.

$y = \frac{- 2 x}{- 2 \cdot 5}$

Rewrite the expression.

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