Solve by Addition/Elimination x-y=2 2x+3y=14

$x - y = 2$ $2 x + 3 y = 14$

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

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

$2 x + 3 y = 14$

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$2 x + 3 y = 14$

Multiply $- 1$ by $- 2$ .

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

$2 x + 3 y = 14$

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

$2 x + 3 y = 14$

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

$2 x + 3 y = 14$

Simplify the right side.

Multiply $- 2$ by $2$ .

$- 2 x + 2 y = - 4$

$2 x + 3 y = 14$

$- 2 x + 2 y = - 4$

$2 x + 3 y = 14$

$- 2 x + 2 y = - 4$

$2 x + 3 y = 14$

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

	$-$	$2$	$x$	$+$	$2$	$y$	$=$	$-$	$4$
$+$		$2$	$x$	$+$	$3$	$y$	$=$	$1$	$4$
					$5$	$y$	$=$	$1$	$0$

Divide each term in $5 y = 10$ by $5$ and simplify.

Divide each term in $5 y = 10$ by $5$ .

$\frac{5 y}{5} = \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{10}{5}$

Divide $y$ by $1$ .

$y = \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$y = 2$

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 $x$ .

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

Multiply $2$ by $2$ .

$- 2 x + 4 = - 4$

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

Subtract $4$ from both sides of the equation.

$- 2 x = - 4 - 4$

Subtract $4$ from $- 4$ .

$- 2 x = - 8$

Divide each term in $- 2 x = - 8$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 8$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 8}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 2}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$x = 4$

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

$(4, 2)$

The result can be shown in multiple forms.

Point Form:

$(4, 2)$

Equation Form:

$x = 4, y = 2$

Solve by Addition/Elimination x-y=2 2x+3y=14

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