Solve by Addition/Elimination 2x+y=-3 3x-y=-17

$2 x + y = - 3$ $3 x - y = - 17$

Step 1

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

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 20$ by $5$ .

$x = - 4$

Step 3

Substitute the value found for $x$ into one of the original equations, then solve for $y$ .

Substitute the value found for $x$ into one of the original equations to solve for $y$ .

$2 (- 4) + y = - 3$

Multiply $2$ by $- 4$ .

$- 8 + y = - 3$

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

Add $8$ to both sides of the equation.

$y = - 3 + 8$

Add $- 3$ and $8$ .

$y = 5$

Step 4

The solution to the independent system of equations can be represented as a point.

$(- 4, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 4, 5)$

Equation Form:

$x = - 4, y = 5$

Step 6