Solve by Addition/Elimination -8x+3y=-5 8x-2y=6

$- 8 x + 3 y = - 5$ $8 x - 2 y = 6$

Step 1

Multiply each equation by the value that makes the coefficients of $y$ opposite.

$(2) \cdot (- 8 x + 3 y) = (2) (- 5)$

$(3) \cdot (8 x - 2 y) = (3) (6)$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (- 8 x + 3 y)$ .

Apply the distributive property.

$2 (- 8 x) + 2 (3 y) = (2) (- 5)$

$(3) \cdot (8 x - 2 y) = (3) (6)$

Multiply.

Multiply $- 8$ by $2$ .

$- 16 x + 2 (3 y) = (2) (- 5)$

$(3) \cdot (8 x - 2 y) = (3) (6)$

Multiply $3$ by $2$ .

$- 16 x + 6 y = (2) (- 5)$

$(3) \cdot (8 x - 2 y) = (3) (6)$

$- 16 x + 6 y = (2) (- 5)$

$(3) \cdot (8 x - 2 y) = (3) (6)$

$- 16 x + 6 y = (2) (- 5)$

$(3) \cdot (8 x - 2 y) = (3) (6)$

$- 16 x + 6 y = (2) (- 5)$

$(3) \cdot (8 x - 2 y) = (3) (6)$

Simplify the right side.

Multiply $2$ by $- 5$ .

$- 16 x + 6 y = - 10$

$(3) \cdot (8 x - 2 y) = (3) (6)$

$- 16 x + 6 y = - 10$

$(3) \cdot (8 x - 2 y) = (3) (6)$

Simplify the left side.

Simplify $(3) \cdot (8 x - 2 y)$ .

Apply the distributive property.

$- 16 x + 6 y = - 10$

$3 (8 x) + 3 (- 2 y) = (3) (6)$

Multiply.

Multiply $8$ by $3$ .

$- 16 x + 6 y = - 10$

$24 x + 3 (- 2 y) = (3) (6)$

Multiply $- 2$ by $3$ .

$- 16 x + 6 y = - 10$

$24 x - 6 y = (3) (6)$

$- 16 x + 6 y = - 10$

$24 x - 6 y = (3) (6)$

$- 16 x + 6 y = - 10$

$24 x - 6 y = (3) (6)$

$- 16 x + 6 y = - 10$

$24 x - 6 y = (3) (6)$

Simplify the right side.

Multiply $3$ by $6$ .

$- 16 x + 6 y = - 10$

$24 x - 6 y = 18$

$- 16 x + 6 y = - 10$

$24 x - 6 y = 18$

$- 16 x + 6 y = - 10$

$24 x - 6 y = 18$

Step 3

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

	$-$	$1$	$6$	$x$	$+$	$6$	$y$	$=$	$-$	$1$	$0$
$+$		$2$	$4$	$x$	$-$	$6$	$y$	$=$		$1$	$8$
			$8$	$x$				$=$			$8$

Step 4

Divide each term in $8 x = 8$ by $8$ and simplify.

Divide each term in $8 x = 8$ by $8$ .

$\frac{8 x}{8} = \frac{8}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{8}{8}$

Divide $x$ by $1$ .

$x = \frac{8}{8}$

Simplify the right side.

Divide $8$ by $8$ .

$x = 1$

Step 5

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 $y$ .

$- 16 \cdot 1 + 6 y = - 10$

Multiply $- 16$ by $1$ .

$- 16 + 6 y = - 10$

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

Add $16$ to both sides of the equation.

$6 y = - 10 + 16$

Add $- 10$ and $16$ .

$6 y = 6$

Divide each term in $6 y = 6$ by $6$ and simplify.

Divide each term in $6 y = 6$ by $6$ .

$\frac{6 y}{6} = \frac{6}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{6}{6}$

Divide $y$ by $1$ .

$y = \frac{6}{6}$

Simplify the right side.

Divide $6$ by $6$ .

$y = 1$

Step 6

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

$(1, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(1, 1)$

Equation Form:

$x = 1, y = 1$

Step 8

Solve by Addition/Elimination -8x+3y=-5 8x-2y=6

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