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

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

Step 1

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

$(6) \cdot (x + 3 y) = (6) (11)$

$- 6 x + 2 y = - 6$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$6 x + 6 (3 y) = (6) (11)$

$- 6 x + 2 y = - 6$

Multiply $3$ by $6$ .

$6 x + 18 y = (6) (11)$

$- 6 x + 2 y = - 6$

$6 x + 18 y = (6) (11)$

$- 6 x + 2 y = - 6$

$6 x + 18 y = (6) (11)$

$- 6 x + 2 y = - 6$

Simplify the right side.

Multiply $6$ by $11$ .

$6 x + 18 y = 66$

$- 6 x + 2 y = - 6$

$6 x + 18 y = 66$

$- 6 x + 2 y = - 6$

$6 x + 18 y = 66$

$- 6 x + 2 y = - 6$

Step 3

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

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

Step 4

Divide each term in $20 y = 60$ by $20$ and simplify.

Divide each term in $20 y = 60$ by $20$ .

$\frac{20 y}{20} = \frac{60}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 y}{20} = \frac{60}{20}$

Divide $y$ by $1$ .

$y = \frac{60}{20}$

Simplify the right side.

Divide $60$ by $20$ .

$y = 3$

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 $x$ .

$6 x + 18 (3) = 66$

Multiply $18$ by $3$ .

$6 x + 54 = 66$

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

Subtract $54$ from both sides of the equation.

$6 x = 66 - 54$

Subtract $54$ from $66$ .

$6 x = 12$

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

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

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $12$ by $6$ .

$x = 2$

Step 6

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

$(2, 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$

Step 8

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

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