Solve for y 10x+5y=5x+20

$10 x + 5 y = 5 x + 20$

Step 1

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

Subtract $10 x$ from both sides of the equation.

$5 y = 5 x + 20 - 10 x$

Subtract $10 x$ from $5 x$ .

$5 y = - 5 x + 20$

Step 2

Divide each term in $5 y = - 5 x + 20$ by $5$ and simplify.

Divide each term in $5 y = - 5 x + 20$ by $5$ .

$\frac{5 y}{5} = \frac{- 5 x}{5} + \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 5 x}{5} + \frac{20}{5}$

Divide $y$ by $1$ .

$y = \frac{- 5 x}{5} + \frac{20}{5}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 5$ and $5$ .

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

$y = \frac{5 (- x)}{5} + \frac{20}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$y = \frac{5 (- x)}{5 (1)} + \frac{20}{5}$

Cancel the common factor.

$y = \frac{5 (- x)}{5 \cdot 1} + \frac{20}{5}$

Rewrite the expression.

$y = \frac{- x}{1} + \frac{20}{5}$

Divide $- x$ by $1$ .

$y = - x + \frac{20}{5}$

Divide $20$ by $5$ .

$y = - x + 4$