Solve by Addition/Elimination -8x+3y=7 , 13x-3y=-17

$- 8 x + 3 y = 7$ , $13 x - 3 y = - 17$

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

Divide each term in $5 x = - 10$ by $5$ and simplify.

Divide each term in $5 x = - 10$ by $5$ .

$\frac{5 x}{5} = \frac{- 10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 10}{5}$

Divide $x$ by $1$ .

$x = \frac{- 10}{5}$

Simplify the right side.

Divide $- 10$ by $5$ .

$x = - 2$

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 $y$ .

$- 8 \cdot - 2 + 3 y = 7$

Multiply $- 8$ by $- 2$ .

$16 + 3 y = 7$

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

Subtract $16$ from both sides of the equation.

$3 y = 7 - 16$

Subtract $16$ from $7$ .

$3 y = - 9$

Divide each term in $3 y = - 9$ by $3$ and simplify.

Divide each term in $3 y = - 9$ by $3$ .

$\frac{3 y}{3} = \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 9}{3}$

Divide $y$ by $1$ .

$y = \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$y = - 3$

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

$(- 2, - 3)$

The result can be shown in multiple forms.

Point Form:

$(- 2, - 3)$

Equation Form:

$x = - 2, y = - 3$