Solve by Addition/Elimination -6x+6y=6 3x-4y=3

$- 6 x + 6 y = 6$ $3 x - 4 y = 3$

Step 1

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

$- 6 x + 6 y = 6$

$(2) \cdot (3 x - 4 y) = (2) (3)$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (3 x - 4 y)$ .

Apply the distributive property.

$- 6 x + 6 y = 6$

$2 (3 x) + 2 (- 4 y) = (2) (3)$

Multiply.

Multiply $3$ by $2$ .

$- 6 x + 6 y = 6$

$6 x + 2 (- 4 y) = (2) (3)$

Multiply $- 4$ by $2$ .

$- 6 x + 6 y = 6$

$6 x - 8 y = (2) (3)$

$- 6 x + 6 y = 6$

$6 x - 8 y = (2) (3)$

$- 6 x + 6 y = 6$

$6 x - 8 y = (2) (3)$

$- 6 x + 6 y = 6$

$6 x - 8 y = (2) (3)$

Simplify the right side.

Multiply $2$ by $3$ .

$- 6 x + 6 y = 6$

$6 x - 8 y = 6$

$- 6 x + 6 y = 6$

$6 x - 8 y = 6$

$- 6 x + 6 y = 6$

$6 x - 8 y = 6$

Step 3

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

	$-$	$6$	$x$	$+$	$6$	$y$	$=$	$6$
$+$		$6$	$x$	$-$	$8$	$y$	$=$	$6$
				$-$	$2$	$y$	$=$	$1$	$2$

Step 4

Divide each term in $- 2 y = 12$ by $- 2$ and simplify.

Divide each term in $- 2 y = 12$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{12}{- 2}$

Divide $y$ by $1$ .

$y = \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$y = - 6$

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 $x$ .

$- 6 x + 6 (- 6) = 6$

Multiply $6$ by $- 6$ .

$- 6 x - 36 = 6$

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

Add $36$ to both sides of the equation.

$- 6 x = 6 + 36$

Add $6$ and $36$ .

$- 6 x = 42$

Divide each term in $- 6 x = 42$ by $- 6$ and simplify.

Divide each term in $- 6 x = 42$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{42}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{42}{- 6}$

Divide $x$ by $1$ .

$x = \frac{42}{- 6}$

Simplify the right side.

Divide $42$ by $- 6$ .

$x = - 7$

Step 6

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

$(- 7, - 6)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 7, - 6)$

Equation Form:

$x = - 7, y = - 6$

Step 8

Solve by Addition/Elimination -6x+6y=6 3x-4y=3

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