Solve by Addition/Elimination 6x+9y=-3 6x+5y=9

$6 x + 9 y = - 3$ $6 x + 5 y = 9$

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

$(- 1) \cdot (6 x + 9 y) = (- 1) (- 3)$

$6 x + 5 y = 9$

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (6 x + 9 y)$ .

Apply the distributive property.

$- 1 (6 x) - 1 (9 y) = (- 1) (- 3)$

$6 x + 5 y = 9$

Multiply.

Multiply $6$ by $- 1$ .

$- 6 x - 1 (9 y) = (- 1) (- 3)$

$6 x + 5 y = 9$

Multiply $9$ by $- 1$ .

$- 6 x - 9 y = (- 1) (- 3)$

$6 x + 5 y = 9$

$- 6 x - 9 y = (- 1) (- 3)$

$6 x + 5 y = 9$

$- 6 x - 9 y = (- 1) (- 3)$

$6 x + 5 y = 9$

$- 6 x - 9 y = (- 1) (- 3)$

$6 x + 5 y = 9$

Simplify the right side.

Multiply $- 1$ by $- 3$ .

$- 6 x - 9 y = 3$

$6 x + 5 y = 9$

$- 6 x - 9 y = 3$

$6 x + 5 y = 9$

$- 6 x - 9 y = 3$

$6 x + 5 y = 9$

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

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

Divide each term in $- 4 y = 12$ by $- 4$ and simplify.

Divide each term in $- 4 y = 12$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{12}{- 4}$

Divide $y$ by $1$ .

$y = \frac{12}{- 4}$

Simplify the right side.

Divide $12$ by $- 4$ .

$y = - 3$

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 $x$ .

$- 6 x - 9 \cdot - 3 = 3$

Multiply $- 9$ by $- 3$ .

$- 6 x + 27 = 3$

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

Subtract $27$ from both sides of the equation.

$- 6 x = 3 - 27$

Subtract $27$ from $3$ .

$- 6 x = - 24$

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 $- 6$ .

$x = 4$

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

$(4, - 3)$

The result can be shown in multiple forms.

Point Form:

$(4, - 3)$

Equation Form:

$x = 4, y = - 3$

Solve by Addition/Elimination 6x+9y=-3 6x+5y=9

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