Solve by Addition/Elimination -2x+3y=-7 3x+y=16

$- 2 x + 3 y = - 7$ $3 x + y = 16$

Step 1

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

$- 2 x + 3 y = - 7$

$(- 3) \cdot (3 x + y) = (- 3) (16)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 2 x + 3 y = - 7$

$- 3 (3 x) - 3 y = (- 3) (16)$

Multiply $3$ by $- 3$ .

$- 2 x + 3 y = - 7$

$- 9 x - 3 y = (- 3) (16)$

$- 2 x + 3 y = - 7$

$- 9 x - 3 y = (- 3) (16)$

$- 2 x + 3 y = - 7$

$- 9 x - 3 y = (- 3) (16)$

Simplify the right side.

Multiply $- 3$ by $16$ .

$- 2 x + 3 y = - 7$

$- 9 x - 3 y = - 48$

$- 2 x + 3 y = - 7$

$- 9 x - 3 y = - 48$

$- 2 x + 3 y = - 7$

$- 9 x - 3 y = - 48$

Step 3

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

		$-$	$2$	$x$	$+$	$3$	$y$	$=$		$-$	$7$
$+$		$-$	$9$	$x$	$-$	$3$	$y$	$=$	$-$	$4$	$8$
	$-$	$1$	$1$	$x$				$=$	$-$	$5$	$5$

Step 4

Divide each term in $- 11 x = - 55$ by $- 11$ and simplify.

Divide each term in $- 11 x = - 55$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{- 55}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{- 55}{- 11}$

Divide $x$ by $1$ .

$x = \frac{- 55}{- 11}$

Simplify the right side.

Divide $- 55$ by $- 11$ .

$x = 5$

Step 5

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 $y$ .

$- 2 \cdot 5 + 3 y = - 7$

Multiply $- 2$ by $5$ .

$- 10 + 3 y = - 7$

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

Add $10$ to both sides of the equation.

$3 y = - 7 + 10$

Add $- 7$ and $10$ .

$3 y = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $3$ by $3$ .

$y = 1$

Step 6

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

$(5, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(5, 1)$

Equation Form:

$x = 5, y = 1$

Step 8

Solve by Addition/Elimination -2x+3y=-7 3x+y=16

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