Solve by Addition/Elimination 6x-4y=5 6x+7y=-17

$6 x - 4 y = 5$ $6 x + 7 y = - 17$

Step 1

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

$(- 1) \cdot (6 x - 4 y) = (- 1) (5)$

$6 x + 7 y = - 17$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (6 x - 4 y)$ .

Apply the distributive property.

$- 1 (6 x) - 1 (- 4 y) = (- 1) (5)$

$6 x + 7 y = - 17$

Multiply.

Multiply $6$ by $- 1$ .

$- 6 x - 1 (- 4 y) = (- 1) (5)$

$6 x + 7 y = - 17$

Multiply $- 4$ by $- 1$ .

$- 6 x + 4 y = (- 1) (5)$

$6 x + 7 y = - 17$

$- 6 x + 4 y = (- 1) (5)$

$6 x + 7 y = - 17$

$- 6 x + 4 y = (- 1) (5)$

$6 x + 7 y = - 17$

$- 6 x + 4 y = (- 1) (5)$

$6 x + 7 y = - 17$

Simplify the right side.

Multiply $- 1$ by $5$ .

$- 6 x + 4 y = - 5$

$6 x + 7 y = - 17$

$- 6 x + 4 y = - 5$

$6 x + 7 y = - 17$

$- 6 x + 4 y = - 5$

$6 x + 7 y = - 17$

Step 3

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

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

Step 4

Divide each term in $11 y = - 22$ by $11$ and simplify.

Divide each term in $11 y = - 22$ by $11$ .

$\frac{11 y}{11} = \frac{- 22}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} = \frac{- 22}{11}$

Divide $y$ by $1$ .

$y = \frac{- 22}{11}$

Simplify the right side.

Divide $- 22$ by $11$ .

$y = - 2$

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 $x$ .

$- 6 x + 4 (- 2) = - 5$

Multiply $4$ by $- 2$ .

$- 6 x - 8 = - 5$

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

Add $8$ to both sides of the equation.

$- 6 x = - 5 + 8$

Add $- 5$ and $8$ .

$- 6 x = 3$

Divide each term in $- 6 x = 3$ by $- 6$ and simplify.

Divide each term in $- 6 x = 3$ by $- 6$ .

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

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $3$ and $- 6$ .

Factor $3$ out of $3$ .

$x = \frac{3 (1)}{- 6}$

Cancel the common factors.

Factor $3$ out of $- 6$ .

$x = \frac{3 \cdot 1}{3 \cdot - 2}$

Cancel the common factor.

$x = \frac{3 \cdot 1}{3 \cdot - 2}$

Rewrite the expression.

$x = \frac{1}{- 2}$

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 6

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

$(- \frac{1}{2}, - 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- \frac{1}{2}, - 2)$

Equation Form:

$x = - \frac{1}{2}, y = - 2$

Step 8

Solve by Addition/Elimination 6x-4y=5 6x+7y=-17

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