Solve by Addition/Elimination 5x+4y=-14 3x+6y=6

$5 x + 4 y = - 14$ $3 x + 6 y = 6$

Step 1

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

$(- 3) \cdot (5 x + 4 y) = (- 3) (- 14)$

$(2) \cdot (3 x + 6 y) = (2) (6)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (5 x + 4 y)$ .

Apply the distributive property.

$- 3 (5 x) - 3 (4 y) = (- 3) (- 14)$

$(2) \cdot (3 x + 6 y) = (2) (6)$

Multiply.

Multiply $5$ by $- 3$ .

$- 15 x - 3 (4 y) = (- 3) (- 14)$

$(2) \cdot (3 x + 6 y) = (2) (6)$

Multiply $4$ by $- 3$ .

$- 15 x - 12 y = (- 3) (- 14)$

$(2) \cdot (3 x + 6 y) = (2) (6)$

$- 15 x - 12 y = (- 3) (- 14)$

$(2) \cdot (3 x + 6 y) = (2) (6)$

$- 15 x - 12 y = (- 3) (- 14)$

$(2) \cdot (3 x + 6 y) = (2) (6)$

$- 15 x - 12 y = (- 3) (- 14)$

$(2) \cdot (3 x + 6 y) = (2) (6)$

Simplify the right side.

Multiply $- 3$ by $- 14$ .

$- 15 x - 12 y = 42$

$(2) \cdot (3 x + 6 y) = (2) (6)$

$- 15 x - 12 y = 42$

$(2) \cdot (3 x + 6 y) = (2) (6)$

Simplify the left side.

Simplify $(2) \cdot (3 x + 6 y)$ .

Apply the distributive property.

$- 15 x - 12 y = 42$

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

Multiply.

Multiply $3$ by $2$ .

$- 15 x - 12 y = 42$

$6 x + 2 (6 y) = (2) (6)$

Multiply $6$ by $2$ .

$- 15 x - 12 y = 42$

$6 x + 12 y = (2) (6)$

$- 15 x - 12 y = 42$

$6 x + 12 y = (2) (6)$

$- 15 x - 12 y = 42$

$6 x + 12 y = (2) (6)$

$- 15 x - 12 y = 42$

$6 x + 12 y = (2) (6)$

Simplify the right side.

Multiply $2$ by $6$ .

$- 15 x - 12 y = 42$

$6 x + 12 y = 12$

$- 15 x - 12 y = 42$

$6 x + 12 y = 12$

$- 15 x - 12 y = 42$

$6 x + 12 y = 12$

Step 3

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

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

Step 4

Divide each term in $- 9 x = 54$ by $- 9$ and simplify.

Divide each term in $- 9 x = 54$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{54}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{54}{- 9}$

Divide $x$ by $1$ .

$x = \frac{54}{- 9}$

Simplify the right side.

Divide $54$ by $- 9$ .

$x = - 6$

Step 5

Substitute the value found for $x$ into one of the original equations, then solve for $y$ .

Substitute the value found for $x$ into one of the original equations to solve for $y$ .

$- 15 \cdot - 6 - 12 y = 42$

Multiply $- 15$ by $- 6$ .

$90 - 12 y = 42$

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

Subtract $90$ from both sides of the equation.

$- 12 y = 42 - 90$

Subtract $90$ from $42$ .

$- 12 y = - 48$

Divide each term in $- 12 y = - 48$ by $- 12$ and simplify.

Divide each term in $- 12 y = - 48$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{- 48}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{- 48}{- 12}$

Divide $y$ by $1$ .

$y = \frac{- 48}{- 12}$

Simplify the right side.

Divide $- 48$ by $- 12$ .

$y = 4$

Step 6

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

$(- 6, 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 6, 4)$

Equation Form:

$x = - 6, y = 4$

Step 8

Solve by Addition/Elimination 5x+4y=-14 3x+6y=6

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