Solve by Addition/Elimination -2x-6y=-16 , 4x-6y=-58

$- 2 x - 6 y = - 16$ , $4 x - 6 y = - 58$

Step 1

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

$(2) \cdot (- 2 x - 6 y) = (2) (- 16)$

$4 x - 6 y = - 58$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$4 x - 6 y = - 58$

Multiply.

Multiply $- 2$ by $2$ .

$- 4 x + 2 (- 6 y) = (2) (- 16)$

$4 x - 6 y = - 58$

Multiply $- 6$ by $2$ .

$- 4 x - 12 y = (2) (- 16)$

$4 x - 6 y = - 58$

$- 4 x - 12 y = (2) (- 16)$

$4 x - 6 y = - 58$

$- 4 x - 12 y = (2) (- 16)$

$4 x - 6 y = - 58$

$- 4 x - 12 y = (2) (- 16)$

$4 x - 6 y = - 58$

Simplify the right side.

Multiply $2$ by $- 16$ .

$- 4 x - 12 y = - 32$

$4 x - 6 y = - 58$

$- 4 x - 12 y = - 32$

$4 x - 6 y = - 58$

$- 4 x - 12 y = - 32$

$4 x - 6 y = - 58$

Step 3

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

	$-$	$4$	$x$	$-$	$1$	$2$	$y$	$=$	$-$	$3$	$2$
$+$		$4$	$x$		$-$	$6$	$y$	$=$	$-$	$5$	$8$
				$-$	$1$	$8$	$y$	$=$	$-$	$9$	$0$

Step 4

Divide each term in $- 18 y = - 90$ by $- 18$ and simplify.

Divide each term in $- 18 y = - 90$ by $- 18$ .

$\frac{- 18 y}{- 18} = \frac{- 90}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 y}{- 18} = \frac{- 90}{- 18}$

Divide $y$ by $1$ .

$y = \frac{- 90}{- 18}$

Simplify the right side.

Divide $- 90$ by $- 18$ .

$y = 5$

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 $x$ .

$- 4 x - 12 \cdot 5 = - 32$

Multiply $- 12$ by $5$ .

$- 4 x - 60 = - 32$

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

Add $60$ to both sides of the equation.

$- 4 x = - 32 + 60$

Add $- 32$ and $60$ .

$- 4 x = 28$

Divide each term in $- 4 x = 28$ by $- 4$ and simplify.

Divide each term in $- 4 x = 28$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{28}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{28}{- 4}$

Divide $x$ by $1$ .

$x = \frac{28}{- 4}$

Simplify the right side.

Divide $28$ by $- 4$ .

$x = - 7$

Step 6

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

$(- 7, 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 7, 5)$

Equation Form:

$x = - 7, y = 5$

Step 8

Solve by Addition/Elimination -2x-6y=-16 , 4x-6y=-58

Related Questions

Support LCMGCF.com by disabling your adblocker.