Solve by Linear Combination p+q=0 q-p=8

$p + q = 0$ $q - p = 8$

Simplify the left side.

Reorder $q$ and $- p$ .

$- p + q = 8$

$p + q = 0$

$- p + q = 8$

$p + q = 0$

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

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $q$ by $1$ .

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

Simplify the right side.

Divide $8$ by $2$ .

$q = 4$

Substitute the value found for $q$ into one of the original equations, then solve for $p$ .

Substitute the value found for $q$ into one of the original equations to solve for $p$ .

$p + 4 = 0$

Subtract $4$ from both sides of the equation.

$p = - 4$

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

$q = 4$

$p = - 4$