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

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

Step 1

Subtract $y$ from both sides of the equation.

$2 x - y = 1$

$- 3 x + 2 y = 2$

Step 2

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

$(2) \cdot (2 x - y) = (2) (1)$

$- 3 x + 2 y = 2$

Step 3

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$- 3 x + 2 y = 2$

Multiply.

Multiply $2$ by $2$ .

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

$- 3 x + 2 y = 2$

Multiply $- 1$ by $2$ .

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

$- 3 x + 2 y = 2$

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

$- 3 x + 2 y = 2$

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

$- 3 x + 2 y = 2$

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

$- 3 x + 2 y = 2$

Simplify the right side.

Multiply $2$ by $1$ .

$4 x - 2 y = 2$

$- 3 x + 2 y = 2$

$4 x - 2 y = 2$

$- 3 x + 2 y = 2$

$4 x - 2 y = 2$

$- 3 x + 2 y = 2$

Step 4

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

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

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 $y$ .

$4 (4) - 2 y = 2$

Multiply $4$ by $4$ .

$16 - 2 y = 2$

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

Subtract $16$ from both sides of the equation.

$- 2 y = 2 - 16$

Subtract $16$ from $2$ .

$- 2 y = - 14$

Divide each term in $- 2 y = - 14$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 14$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 14}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 14}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- 14}{- 2}$

Simplify the right side.

Divide $- 14$ by $- 2$ .

$y = 7$

Step 6

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

$(4, 7)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, 7)$

Equation Form:

$x = 4, y = 7$

Step 8

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

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