Solve by Addition/Elimination 6x+7y=-4 6x+4y=8

$6 x + 7 y = - 4$ $6 x + 4 y = 8$

Step 1

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

$(- 1) \cdot (6 x + 7 y) = (- 1) (- 4)$

$6 x + 4 y = 8$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (6 x + 7 y)$ .

Apply the distributive property.

$- 1 (6 x) - 1 (7 y) = (- 1) (- 4)$

$6 x + 4 y = 8$

Multiply.

Multiply $6$ by $- 1$ .

$- 6 x - 1 (7 y) = (- 1) (- 4)$

$6 x + 4 y = 8$

Multiply $7$ by $- 1$ .

$- 6 x - 7 y = (- 1) (- 4)$

$6 x + 4 y = 8$

$- 6 x - 7 y = (- 1) (- 4)$

$6 x + 4 y = 8$

$- 6 x - 7 y = (- 1) (- 4)$

$6 x + 4 y = 8$

$- 6 x - 7 y = (- 1) (- 4)$

$6 x + 4 y = 8$

Simplify the right side.

Multiply $- 1$ by $- 4$ .

$- 6 x - 7 y = 4$

$6 x + 4 y = 8$

$- 6 x - 7 y = 4$

$6 x + 4 y = 8$

$- 6 x - 7 y = 4$

$6 x + 4 y = 8$

Step 3

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

	$-$	$6$	$x$	$-$	$7$	$y$	$=$	$4$
$+$		$6$	$x$	$+$	$4$	$y$	$=$	$8$
				$-$	$3$	$y$	$=$	$1$	$2$

Step 4

Divide each term in $- 3 y = 12$ by $- 3$ and simplify.

Divide each term in $- 3 y = 12$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{12}{- 3}$

Divide $y$ by $1$ .

$y = \frac{12}{- 3}$

Simplify the right side.

Divide $12$ by $- 3$ .

$y = - 4$

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 $x$ .

$- 6 x - 7 \cdot - 4 = 4$

Multiply $- 7$ by $- 4$ .

$- 6 x + 28 = 4$

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

Subtract $28$ from both sides of the equation.

$- 6 x = 4 - 28$

Subtract $28$ from $4$ .

$- 6 x = - 24$

Divide each term in $- 6 x = - 24$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 24$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 24}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 24}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 6}$

Simplify the right side.

Divide $- 24$ by $- 6$ .

$x = 4$

Step 6

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

$(4, - 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, - 4)$

Equation Form:

$x = 4, y = - 4$

Step 8

Solve by Addition/Elimination 6x+7y=-4 6x+4y=8

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