Solve by Addition/Elimination x=3y+11 2x-3y=16

$x = 3 y + 11$ $2 x - 3 y = 16$

Subtract $3 y$ from both sides of the equation.

$x - 3 y = 11$

$2 x - 3 y = 16$

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

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

$2 x - 3 y = 16$

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$2 x - 3 y = 16$

Multiply $- 3$ by $- 2$ .

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

$2 x - 3 y = 16$

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

$2 x - 3 y = 16$

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

$2 x - 3 y = 16$

Simplify the right side.

Multiply $- 2$ by $11$ .

$- 2 x + 6 y = - 22$

$2 x - 3 y = 16$

$- 2 x + 6 y = - 22$

$2 x - 3 y = 16$

$- 2 x + 6 y = - 22$

$2 x - 3 y = 16$

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

	$-$	$2$	$x$	$+$	$6$	$y$	$=$	$-$	$2$	$2$
$+$		$2$	$x$	$-$	$3$	$y$	$=$		$1$	$6$
					$3$	$y$	$=$		$-$	$6$

Divide each term in $3 y = - 6$ by $3$ and simplify.

Divide each term in $3 y = - 6$ by $3$ .

$\frac{3 y}{3} = \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 6}{3}$

Divide $y$ by $1$ .

$y = \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$y = - 2$

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 $x$ .

$- 2 x + 6 (- 2) = - 22$

Multiply $6$ by $- 2$ .

$- 2 x - 12 = - 22$

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

Add $12$ to both sides of the equation.

$- 2 x = - 22 + 12$

Add $- 22$ and $12$ .

$- 2 x = - 10$

Divide each term in $- 2 x = - 10$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 10$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 10}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 2}$

Simplify the right side.

Divide $- 10$ by $- 2$ .

$x = 5$

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

$(5, - 2)$

The result can be shown in multiple forms.

Point Form:

$(5, - 2)$

Equation Form:

$x = 5, y = - 2$

Solve by Addition/Elimination x=3y+11 2x-3y=16

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