Solve by Addition/Elimination -v+w=7 v+w=1

$- v + w = 7$ $v + w = 1$

Add the two equations together to eliminate $v$ from the system.

Divide each term in $2 w = 8$ by $2$ and simplify.

Divide each term in $2 w = 8$ by $2$ .

$\frac{2 w}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 w}{2} = \frac{8}{2}$

Divide $w$ by $1$ .

$w = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$w = 4$

Substitute the value found for $w$ into one of the original equations, then solve for $v$ .

Substitute the value found for $w$ into one of the original equations to solve for $v$ .

$- v + 4 = 7$

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

Subtract $4$ from both sides of the equation.

$- v = 7 - 4$

Subtract $4$ from $7$ .

$- v = 3$

Divide each term in $- v = 3$ by $- 1$ and simplify.

Divide each term in $- v = 3$ by $- 1$ .

$\frac{- v}{- 1} = \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{v}{1} = \frac{3}{- 1}$

Divide $v$ by $1$ .

$v = \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$v = - 3$

This is the final solution to the independent system of equations.

$w = 4$

$v = - 3$