Solve for v 4u+8v=-3u+2v

$4 u + 8 v = - 3 u + 2 v$

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

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

$4 u + 8 v - 2 v = - 3 u$

Subtract $2 v$ from $8 v$ .

$4 u + 6 v = - 3 u$

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

Subtract $4 u$ from both sides of the equation.

$6 v = - 3 u - 4 u$

Subtract $4 u$ from $- 3 u$ .

$6 v = - 7 u$

Divide each term in $6 v = - 7 u$ by $6$ and simplify.

Divide each term in $6 v = - 7 u$ by $6$ .

$\frac{6 v}{6} = \frac{- 7 u}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 v}{6} = \frac{- 7 u}{6}$

Divide $v$ by $1$ .

$v = \frac{- 7 u}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$v = - \frac{7 u}{6}$