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

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

Step 1

Simplify the left side.

Reorder $y$ and $- 3 x$ .

$- 3 x + y = 11$

$2 y - x = 2$

$- 3 x + y = 11$

$2 y - x = 2$

Step 2

Simplify the left side.

Reorder $2 y$ and $- x$ .

$- x + 2 y = 2$

$- 3 x + y = 11$

$- x + 2 y = 2$

$- 3 x + y = 11$

Step 3

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

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

$- x + 2 y = 2$

Step 4

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$- x + 2 y = 2$

Multiply $- 3$ by $- 2$ .

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

$- x + 2 y = 2$

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

$- x + 2 y = 2$

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

$- x + 2 y = 2$

Simplify the right side.

Multiply $- 2$ by $11$ .

$6 x - 2 y = - 22$

$- x + 2 y = 2$

$6 x - 2 y = - 22$

$- x + 2 y = 2$

$6 x - 2 y = - 22$

$- x + 2 y = 2$

Step 5

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

	$6$	$x$	$-$	$2$	$y$	$=$	$-$	$2$	$2$
$+$	$-$	$x$	$+$	$2$	$y$	$=$			$2$
	$5$	$x$				$=$	$-$	$2$	$0$

Step 6

Divide each term in $5 x = - 20$ by $5$ and simplify.

Divide each term in $5 x = - 20$ by $5$ .

$\frac{5 x}{5} = \frac{- 20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 20}{5}$

Divide $x$ by $1$ .

$x = \frac{- 20}{5}$

Simplify the right side.

Divide $- 20$ by $5$ .

$x = - 4$

Step 7

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 $y$ .

$6 (- 4) - 2 y = - 22$

Multiply $6$ by $- 4$ .

$- 24 - 2 y = - 22$

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

Add $24$ to both sides of the equation.

$- 2 y = - 22 + 24$

Add $- 22$ and $24$ .

$- 2 y = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $2$ by $- 2$ .

$y = - 1$

Step 8

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

$(- 4, - 1)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(- 4, - 1)$

Equation Form:

$x = - 4, y = - 1$

Step 10

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

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