Solve by Addition/Elimination -4x-2y=-2 and 4x+8y=-24

$- 4 x - 2 y = - 2$ and $4 x + 8 y = - 24$

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

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

Divide each term in $6 y = - 26$ by $6$ and simplify.

Divide each term in $6 y = - 26$ by $6$ .

$\frac{6 y}{6} = \frac{- 26}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 26}{6}$

Divide $y$ by $1$ .

$y = \frac{- 26}{6}$

Simplify the right side.

Cancel the common factor of $- 26$ and $6$ .

Factor $2$ out of $- 26$ .

$y = \frac{2 (- 13)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$y = \frac{2 \cdot - 13}{2 \cdot 3}$

Cancel the common factor.

$y = \frac{2 \cdot - 13}{2 \cdot 3}$

Rewrite the expression.

$y = \frac{- 13}{3}$

Move the negative in front of the fraction.

$y = - \frac{13}{3}$

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 $x$ .

$- 4 x - 2 (- \frac{13}{3}) = - 2$

Multiply $- 2 (- \frac{13}{3})$ .

Multiply $- 1$ by $- 2$ .

$- 4 x + 2 (\frac{13}{3}) = - 2$

Combine $2$ and $\frac{13}{3}$ .

$- 4 x + \frac{2 \cdot 13}{3} = - 2$

Multiply $2$ by $13$ .

$- 4 x + \frac{26}{3} = - 2$

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

Subtract $\frac{26}{3}$ from both sides of the equation.

$- 4 x = - 2 - \frac{26}{3}$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 4 x = - 2 \cdot \frac{3}{3} - \frac{26}{3}$

Combine $- 2$ and $\frac{3}{3}$ .

$- 4 x = \frac{- 2 \cdot 3}{3} - \frac{26}{3}$

Combine the numerators over the common denominator.

$- 4 x = \frac{- 2 \cdot 3 - 26}{3}$

Simplify the numerator.

Multiply $- 2$ by $3$ .

$- 4 x = \frac{- 6 - 26}{3}$

Subtract $26$ from $- 6$ .

$- 4 x = \frac{- 32}{3}$

Move the negative in front of the fraction.

$- 4 x = - \frac{32}{3}$

Divide each term in $- 4 x = - \frac{32}{3}$ by $- 4$ and simplify.

Divide each term in $- 4 x = - \frac{32}{3}$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- \frac{32}{3}}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- \frac{32}{3}}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- \frac{32}{3}}{- 4}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{32}{3} \cdot \frac{1}{- 4}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{32}{3}$ into the numerator.

$x = \frac{- 32}{3} \cdot \frac{1}{- 4}$

Factor $4$ out of $- 32$ .

$x = \frac{4 (- 8)}{3} \cdot \frac{1}{- 4}$

Factor $4$ out of $- 4$ .

$x = \frac{4 \cdot - 8}{3} \cdot \frac{1}{4 \cdot - 1}$

Cancel the common factor.

$x = \frac{4 \cdot - 8}{3} \cdot \frac{1}{4 \cdot - 1}$

Rewrite the expression.

$x = \frac{- 8}{3} \cdot \frac{1}{- 1}$

Multiply $\frac{- 8}{3}$ by $\frac{1}{- 1}$ .

$x = \frac{- 8}{3 \cdot - 1}$

Multiply $3$ by $- 1$ .

$x = \frac{- 8}{- 3}$

Dividing two negative values results in a positive value.

$x = \frac{8}{3}$

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

$(\frac{8}{3}, - \frac{13}{3})$

The result can be shown in multiple forms.

Point Form:

$(\frac{8}{3}, - \frac{13}{3})$

Equation Form:

$x = \frac{8}{3}, y = - \frac{13}{3}$

Solve by Addition/Elimination -4x-2y=-2 and 4x+8y=-24

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