Solve by Addition/Elimination 8x-6y=-20 , -16x+7y=30

$8 x - 6 y = - 20$ , $- 16 x + 7 y = 30$

Step 1

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

$(2) \cdot (8 x - 6 y) = (2) (- 20)$

$- 16 x + 7 y = 30$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (8 x - 6 y)$ .

Apply the distributive property.

$2 (8 x) + 2 (- 6 y) = (2) (- 20)$

$- 16 x + 7 y = 30$

Multiply.

Multiply $8$ by $2$ .

$16 x + 2 (- 6 y) = (2) (- 20)$

$- 16 x + 7 y = 30$

Multiply $- 6$ by $2$ .

$16 x - 12 y = (2) (- 20)$

$- 16 x + 7 y = 30$

$16 x - 12 y = (2) (- 20)$

$- 16 x + 7 y = 30$

$16 x - 12 y = (2) (- 20)$

$- 16 x + 7 y = 30$

$16 x - 12 y = (2) (- 20)$

$- 16 x + 7 y = 30$

Simplify the right side.

Multiply $2$ by $- 20$ .

$16 x - 12 y = - 40$

$- 16 x + 7 y = 30$

$16 x - 12 y = - 40$

$- 16 x + 7 y = 30$

$16 x - 12 y = - 40$

$- 16 x + 7 y = 30$

Step 3

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

		$1$	$6$	$x$	$-$	$1$	$2$	$y$	$=$	$-$	$4$	$0$
$+$	$-$	$1$	$6$	$x$	$+$		$7$	$y$	$=$		$3$	$0$
						$-$	$5$	$y$	$=$	$-$	$1$	$0$

Step 4

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 $- 5$ .

$y = 2$

Step 5

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 $x$ .

$16 x - 12 \cdot 2 = - 40$

Multiply $- 12$ by $2$ .

$16 x - 24 = - 40$

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

Add $24$ to both sides of the equation.

$16 x = - 40 + 24$

Add $- 40$ and $24$ .

$16 x = - 16$

Divide each term in $16 x = - 16$ by $16$ and simplify.

Divide each term in $16 x = - 16$ by $16$ .

$\frac{16 x}{16} = \frac{- 16}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{- 16}{16}$

Divide $x$ by $1$ .

$x = \frac{- 16}{16}$

Simplify the right side.

Divide $- 16$ by $16$ .

$x = - 1$

Step 6

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

$(- 1, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 1, 2)$

Equation Form:

$x = - 1, y = 2$

Step 8

Solve by Addition/Elimination 8x-6y=-20 , -16x+7y=30

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