Solve by Addition/Elimination 3x+2y=4 2y=8-5x

$3 x + 2 y = 4$ $2 y = 8 - 5 x$

Step 1

Simplify the right side.

Reorder $8$ and $- 5 x$ .

$2 y = - 5 x + 8$

$3 x + 2 y = 4$

$2 y = - 5 x + 8$

$3 x + 2 y = 4$

Step 2

Move all terms containing variables to the left side of the equation.

Add $5 x$ to both sides of the equation.

$2 y + 5 x = 8$

$3 x + 2 y = 4$

Reorder $2 y$ and $5 x$ .

$5 x + 2 y = 8$

$3 x + 2 y = 4$

$5 x + 2 y = 8$

$3 x + 2 y = 4$

Step 3

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

$(- 1) \cdot (3 x + 2 y) = (- 1) (4)$

$5 x + 2 y = 8$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (3 x + 2 y)$ .

Apply the distributive property.

$- 1 (3 x) - 1 (2 y) = (- 1) (4)$

$5 x + 2 y = 8$

Multiply.

Multiply $3$ by $- 1$ .

$- 3 x - 1 (2 y) = (- 1) (4)$

$5 x + 2 y = 8$

Multiply $2$ by $- 1$ .

$- 3 x - 2 y = (- 1) (4)$

$5 x + 2 y = 8$

$- 3 x - 2 y = (- 1) (4)$

$5 x + 2 y = 8$

$- 3 x - 2 y = (- 1) (4)$

$5 x + 2 y = 8$

$- 3 x - 2 y = (- 1) (4)$

$5 x + 2 y = 8$

Simplify the right side.

Multiply $- 1$ by $4$ .

$- 3 x - 2 y = - 4$

$5 x + 2 y = 8$

$- 3 x - 2 y = - 4$

$5 x + 2 y = 8$

$- 3 x - 2 y = - 4$

$5 x + 2 y = 8$

Step 5

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

	$-$	$3$	$x$	$-$	$2$	$y$	$=$	$-$	$4$
$+$		$5$	$x$	$+$	$2$	$y$	$=$		$8$
		$2$	$x$				$=$		$4$

Step 6

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$

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 $y$ .

$- 3 \cdot 2 - 2 y = - 4$

Multiply $- 3$ by $2$ .

$- 6 - 2 y = - 4$

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

Add $6$ to both sides of the equation.

$- 2 y = - 4 + 6$

Add $- 4$ and $6$ .

$- 2 y = 2$

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.

$(2, - 1)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 10

Solve by Addition/Elimination 3x+2y=4 2y=8-5x

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