Solve by Addition/Elimination 3x+11y=4 -2x-6y=0

$3 x + 11 y = 4$ $- 2 x - 6 y = 0$

Step 1

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

$(2) \cdot (3 x + 11 y) = (2) (4)$

$(3) \cdot (- 2 x - 6 y) = (3) (0)$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (3 x + 11 y)$ .

Apply the distributive property.

$2 (3 x) + 2 (11 y) = (2) (4)$

$(3) \cdot (- 2 x - 6 y) = (3) (0)$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 (11 y) = (2) (4)$

$(3) \cdot (- 2 x - 6 y) = (3) (0)$

Multiply $11$ by $2$ .

$6 x + 22 y = (2) (4)$

$(3) \cdot (- 2 x - 6 y) = (3) (0)$

$6 x + 22 y = (2) (4)$

$(3) \cdot (- 2 x - 6 y) = (3) (0)$

$6 x + 22 y = (2) (4)$

$(3) \cdot (- 2 x - 6 y) = (3) (0)$

$6 x + 22 y = (2) (4)$

$(3) \cdot (- 2 x - 6 y) = (3) (0)$

Simplify the right side.

Multiply $2$ by $4$ .

$6 x + 22 y = 8$

$(3) \cdot (- 2 x - 6 y) = (3) (0)$

$6 x + 22 y = 8$

$(3) \cdot (- 2 x - 6 y) = (3) (0)$

Simplify the left side.

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

Apply the distributive property.

$6 x + 22 y = 8$

$3 (- 2 x) + 3 (- 6 y) = (3) (0)$

Multiply.

Multiply $- 2$ by $3$ .

$6 x + 22 y = 8$

$- 6 x + 3 (- 6 y) = (3) (0)$

Multiply $- 6$ by $3$ .

$6 x + 22 y = 8$

$- 6 x - 18 y = (3) (0)$

$6 x + 22 y = 8$

$- 6 x - 18 y = (3) (0)$

$6 x + 22 y = 8$

$- 6 x - 18 y = (3) (0)$

$6 x + 22 y = 8$

$- 6 x - 18 y = (3) (0)$

Simplify the right side.

Multiply $3$ by $0$ .

$6 x + 22 y = 8$

$- 6 x - 18 y = 0$

$6 x + 22 y = 8$

$- 6 x - 18 y = 0$

$6 x + 22 y = 8$

$- 6 x - 18 y = 0$

Step 3

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

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

Step 4

Divide each term in $4 y = 8$ by $4$ and simplify.

Divide each term in $4 y = 8$ by $4$ .

$\frac{4 y}{4} = \frac{8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{8}{4}$

Divide $y$ by $1$ .

$y = \frac{8}{4}$

Simplify the right side.

Divide $8$ by $4$ .

$y = 2$

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 $x$ .

$6 x + 22 (2) = 8$

Multiply $22$ by $2$ .

$6 x + 44 = 8$

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

Subtract $44$ from both sides of the equation.

$6 x = 8 - 44$

Subtract $44$ from $8$ .

$6 x = - 36$

Divide each term in $6 x = - 36$ by $6$ and simplify.

Divide each term in $6 x = - 36$ by $6$ .

$\frac{6 x}{6} = \frac{- 36}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 36}{6}$

Divide $x$ by $1$ .

$x = \frac{- 36}{6}$

Simplify the right side.

Divide $- 36$ by $6$ .

$x = - 6$

Step 6

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

$(- 6, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 6, 2)$

Equation Form:

$x = - 6, y = 2$

Step 8

Solve by Addition/Elimination 3x+11y=4 -2x-6y=0

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