Solve by Addition/Elimination 3x-2y=8 2x+5y=-1

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

Step 1

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

$(- 2) \cdot (3 x - 2 y) = (- 2) (8)$

$(3) \cdot (2 x + 5 y) = (3) (- 1)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 2 (3 x) - 2 (- 2 y) = (- 2) (8)$

$(3) \cdot (2 x + 5 y) = (3) (- 1)$

Multiply.

Multiply $3$ by $- 2$ .

$- 6 x - 2 (- 2 y) = (- 2) (8)$

$(3) \cdot (2 x + 5 y) = (3) (- 1)$

Multiply $- 2$ by $- 2$ .

$- 6 x + 4 y = (- 2) (8)$

$(3) \cdot (2 x + 5 y) = (3) (- 1)$

$- 6 x + 4 y = (- 2) (8)$

$(3) \cdot (2 x + 5 y) = (3) (- 1)$

$- 6 x + 4 y = (- 2) (8)$

$(3) \cdot (2 x + 5 y) = (3) (- 1)$

$- 6 x + 4 y = (- 2) (8)$

$(3) \cdot (2 x + 5 y) = (3) (- 1)$

Simplify the right side.

Multiply $- 2$ by $8$ .

$- 6 x + 4 y = - 16$

$(3) \cdot (2 x + 5 y) = (3) (- 1)$

$- 6 x + 4 y = - 16$

$(3) \cdot (2 x + 5 y) = (3) (- 1)$

Simplify the left side.

Simplify $(3) \cdot (2 x + 5 y)$ .

Apply the distributive property.

$- 6 x + 4 y = - 16$

$3 (2 x) + 3 (5 y) = (3) (- 1)$

Multiply.

Multiply $2$ by $3$ .

$- 6 x + 4 y = - 16$

$6 x + 3 (5 y) = (3) (- 1)$

Multiply $5$ by $3$ .

$- 6 x + 4 y = - 16$

$6 x + 15 y = (3) (- 1)$

$- 6 x + 4 y = - 16$

$6 x + 15 y = (3) (- 1)$

$- 6 x + 4 y = - 16$

$6 x + 15 y = (3) (- 1)$

$- 6 x + 4 y = - 16$

$6 x + 15 y = (3) (- 1)$

Simplify the right side.

Multiply $3$ by $- 1$ .

$- 6 x + 4 y = - 16$

$6 x + 15 y = - 3$

$- 6 x + 4 y = - 16$

$6 x + 15 y = - 3$

$- 6 x + 4 y = - 16$

$6 x + 15 y = - 3$

Step 3

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

	$-$	$6$	$x$	$+$		$4$	$y$	$=$	$-$	$1$	$6$
$+$		$6$	$x$	$+$	$1$	$5$	$y$	$=$		$-$	$3$
					$1$	$9$	$y$	$=$	$-$	$1$	$9$

Step 4

Divide each term in $19 y = - 19$ by $19$ and simplify.

Divide each term in $19 y = - 19$ by $19$ .

$\frac{19 y}{19} = \frac{- 19}{19}$

Simplify the left side.

Cancel the common factor of $19$ .

Cancel the common factor.

$\frac{19 y}{19} = \frac{- 19}{19}$

Divide $y$ by $1$ .

$y = \frac{- 19}{19}$

Simplify the right side.

Divide $- 19$ by $19$ .

$y = - 1$

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 $x$ .

$- 6 x + 4 (- 1) = - 16$

Multiply $4$ by $- 1$ .

$- 6 x - 4 = - 16$

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

Add $4$ to both sides of the equation.

$- 6 x = - 16 + 4$

Add $- 16$ and $4$ .

$- 6 x = - 12$

Divide each term in $- 6 x = - 12$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 12$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 12}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 6}$

Simplify the right side.

Divide $- 12$ by $- 6$ .

$x = 2$

Step 6

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

$(2, - 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 8

Solve by Addition/Elimination 3x-2y=8 2x+5y=-1

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