Evaluate Using the Given Value -10=-2y+x*6y-3x+11

$- 10 = - 2 y + x \cdot 6 y - 3 x + 11$

Step 1

Rewrite the equation as $- 2 y + x \cdot (6 y) - 3 x + 11 = - 10$ .

$- 2 y + x \cdot (6 y) - 3 x + 11 = - 10$

Step 2

Rewrite using the commutative property of multiplication.

$- 2 y + 6 x y - 3 x + 11 = - 10$

Step 3

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

Add $3 x$ to both sides of the equation.

$- 2 y + 6 x y + 11 = - 10 + 3 x$

Subtract $11$ from both sides of the equation.

$- 2 y + 6 x y = - 10 + 3 x - 11$

Subtract $11$ from $- 10$ .

$- 2 y + 6 x y = 3 x - 21$

Step 4

Factor $2 y$ out of $- 2 y + 6 x y$ .

Factor $2 y$ out of $- 2 y$ .

$2 y (- 1) + 6 x y = 3 x - 21$

Factor $2 y$ out of $6 x y$ .

$2 y (- 1) + 2 y (3 x) = 3 x - 21$

Factor $2 y$ out of $2 y (- 1) + 2 y (3 x)$ .

$2 y (- 1 + 3 x) = 3 x - 21$

Step 5

Divide each term in $2 y (- 1 + 3 x) = 3 x - 21$ by $2 (- 1 + 3 x)$ and simplify.

Divide each term in $2 y (- 1 + 3 x) = 3 x - 21$ by $2 (- 1 + 3 x)$ .

$\frac{2 y (- 1 + 3 x)}{2 (- 1 + 3 x)} = \frac{3 x}{2 (- 1 + 3 x)} + \frac{- 21}{2 (- 1 + 3 x)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y (- 1 + 3 x)}{2 (- 1 + 3 x)} = \frac{3 x}{2 (- 1 + 3 x)} + \frac{- 21}{2 (- 1 + 3 x)}$

Rewrite the expression.

$\frac{y (- 1 + 3 x)}{- 1 + 3 x} = \frac{3 x}{2 (- 1 + 3 x)} + \frac{- 21}{2 (- 1 + 3 x)}$

Cancel the common factor of $- 1 + 3 x$ .

Cancel the common factor.

$\frac{y (- 1 + 3 x)}{- 1 + 3 x} = \frac{3 x}{2 (- 1 + 3 x)} + \frac{- 21}{2 (- 1 + 3 x)}$

Divide $y$ by $1$ .

$y = \frac{3 x}{2 (- 1 + 3 x)} + \frac{- 21}{2 (- 1 + 3 x)}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{3 x}{2 (- 1 + 3 x)} - \frac{21}{2 (- 1 + 3 x)}$