Solve by Addition/Elimination 5x-3y=-11 2x-6y=-14

$5 x - 3 y = - 11$ $2 x - 6 y = - 14$

Step 1

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

$(- 2) \cdot (5 x - 3 y) = (- 2) (- 11)$

$2 x - 6 y = - 14$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (5 x - 3 y)$ .

Apply the distributive property.

$- 2 (5 x) - 2 (- 3 y) = (- 2) (- 11)$

$2 x - 6 y = - 14$

Multiply.

Multiply $5$ by $- 2$ .

$- 10 x - 2 (- 3 y) = (- 2) (- 11)$

$2 x - 6 y = - 14$

Multiply $- 3$ by $- 2$ .

$- 10 x + 6 y = (- 2) (- 11)$

$2 x - 6 y = - 14$

$- 10 x + 6 y = (- 2) (- 11)$

$2 x - 6 y = - 14$

$- 10 x + 6 y = (- 2) (- 11)$

$2 x - 6 y = - 14$

$- 10 x + 6 y = (- 2) (- 11)$

$2 x - 6 y = - 14$

Simplify the right side.

Multiply $- 2$ by $- 11$ .

$- 10 x + 6 y = 22$

$2 x - 6 y = - 14$

$- 10 x + 6 y = 22$

$2 x - 6 y = - 14$

$- 10 x + 6 y = 22$

$2 x - 6 y = - 14$

Step 3

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

	$-$	$1$	$0$	$x$	$+$	$6$	$y$	$=$		$2$	$2$
$+$			$2$	$x$	$-$	$6$	$y$	$=$	$-$	$1$	$4$
		$-$	$8$	$x$				$=$			$8$

Step 4

Divide each term in $- 8 x = 8$ by $- 8$ and simplify.

Divide each term in $- 8 x = 8$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{8}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{8}{- 8}$

Divide $x$ by $1$ .

$x = \frac{8}{- 8}$

Simplify the right side.

Divide $8$ by $- 8$ .

$x = - 1$

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 $y$ .

$- 10 \cdot - 1 + 6 y = 22$

Multiply $- 10$ by $- 1$ .

$10 + 6 y = 22$

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

Subtract $10$ from both sides of the equation.

$6 y = 22 - 10$

Subtract $10$ from $22$ .

$6 y = 12$

Divide each term in $6 y = 12$ by $6$ and simplify.

Divide each term in $6 y = 12$ by $6$ .

$\frac{6 y}{6} = \frac{12}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{12}{6}$

Divide $y$ by $1$ .

$y = \frac{12}{6}$

Simplify the right side.

Divide $12$ by $6$ .

$y = 2$

Step 6

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

$(- 1, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 1, 2)$

Equation Form:

$x = - 1, y = 2$

Step 8

Solve by Addition/Elimination 5x-3y=-11 2x-6y=-14

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