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

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

Step 1

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

$- 2 x + y = 6$

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

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 2 x + y = 6$

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

Multiply $3$ by $2$ .

$- 2 x + y = 6$

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

$- 2 x + y = 6$

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

$- 2 x + y = 6$

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

Simplify the right side.

Multiply $2$ by $11$ .

$- 2 x + y = 6$

$2 x + 6 y = 22$

$- 2 x + y = 6$

$2 x + 6 y = 22$

$- 2 x + y = 6$

$2 x + 6 y = 22$

Step 3

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

	$-$	$2$	$x$	$+$		$y$	$=$		$6$
$+$		$2$	$x$	$+$	$6$	$y$	$=$	$2$	$2$
					$7$	$y$	$=$	$2$	$8$

Step 4

Divide each term in $7 y = 28$ by $7$ and simplify.

Divide each term in $7 y = 28$ by $7$ .

$\frac{7 y}{7} = \frac{28}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{28}{7}$

Divide $y$ by $1$ .

$y = \frac{28}{7}$

Simplify the right side.

Divide $28$ by $7$ .

$y = 4$

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 $x$ .

$- 2 x + 4 = 6$

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

Subtract $4$ from both sides of the equation.

$- 2 x = 6 - 4$

Subtract $4$ from $6$ .

$- 2 x = 2$

Divide each term in $- 2 x = 2$ by $- 2$ and simplify.

Divide each term in $- 2 x = 2$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{2}{- 2}$

Divide $x$ by $1$ .

$x = \frac{2}{- 2}$

Simplify the right side.

Divide $2$ by $- 2$ .

$x = - 1$

Step 6

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

$(- 1, 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 1, 4)$

Equation Form:

$x = - 1, y = 4$

Step 8

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

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