Solve by Addition/Elimination -5x+3y=6 x-y=4

$- 5 x + 3 y = 6$ $x - y = 4$

Step 1

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

$- 5 x + 3 y = 6$

$(3) \cdot (x - y) = (3) (4)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 5 x + 3 y = 6$

$3 x + 3 (- y) = (3) (4)$

Multiply $- 1$ by $3$ .

$- 5 x + 3 y = 6$

$3 x - 3 y = (3) (4)$

$- 5 x + 3 y = 6$

$3 x - 3 y = (3) (4)$

$- 5 x + 3 y = 6$

$3 x - 3 y = (3) (4)$

Simplify the right side.

Multiply $3$ by $4$ .

$- 5 x + 3 y = 6$

$3 x - 3 y = 12$

$- 5 x + 3 y = 6$

$3 x - 3 y = 12$

$- 5 x + 3 y = 6$

$3 x - 3 y = 12$

Step 3

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

	$-$	$5$	$x$	$+$	$3$	$y$	$=$		$6$
$+$		$3$	$x$	$-$	$3$	$y$	$=$	$1$	$2$
	$-$	$2$	$x$				$=$	$1$	$8$

Step 4

Divide each term in $- 2 x = 18$ by $- 2$ and simplify.

Divide each term in $- 2 x = 18$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{18}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{18}{- 2}$

Divide $x$ by $1$ .

$x = \frac{18}{- 2}$

Simplify the right side.

Divide $18$ by $- 2$ .

$x = - 9$

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 $y$ .

$- 5 \cdot - 9 + 3 y = 6$

Multiply $- 5$ by $- 9$ .

$45 + 3 y = 6$

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

Subtract $45$ from both sides of the equation.

$3 y = 6 - 45$

Subtract $45$ from $6$ .

$3 y = - 39$

Divide each term in $3 y = - 39$ by $3$ and simplify.

Divide each term in $3 y = - 39$ by $3$ .

$\frac{3 y}{3} = \frac{- 39}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 39}{3}$

Divide $y$ by $1$ .

$y = \frac{- 39}{3}$

Simplify the right side.

Divide $- 39$ by $3$ .

$y = - 13$

Step 6

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

$(- 9, - 13)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 9, - 13)$

Equation Form:

$x = - 9, y = - 13$

Step 8

Solve by Addition/Elimination -5x+3y=6 x-y=4

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