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

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $- 10$ by $5$ .

$y = - 2$

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

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

$3 x - 8 \cdot - 2 = 7$

Multiply $- 8$ by $- 2$ .

$3 x + 16 = 7$

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

Subtract $16$ from both sides of the equation.

$3 x = 7 - 16$

Subtract $16$ from $7$ .

$3 x = - 9$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 9$ by $3$ .

$x = - 3$

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

$(- 3, - 2)$

The result can be shown in multiple forms.

Point Form:

$(- 3, - 2)$

Equation Form:

$x = - 3, y = - 2$