Solve by Addition/Elimination x+y=4 2x+3y=9

$x + y = 4$ $2 x + 3 y = 9$

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

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

$2 x + 3 y = 9$

Simplify.

Simplify the left side.

Apply the distributive property.

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

$2 x + 3 y = 9$

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

$2 x + 3 y = 9$

Simplify the right side.

Multiply $- 2$ by $4$ .

$- 2 x - 2 y = - 8$

$2 x + 3 y = 9$

$- 2 x - 2 y = - 8$

$2 x + 3 y = 9$

$- 2 x - 2 y = - 8$

$2 x + 3 y = 9$

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

	$-$	$2$	$x$	$-$	$2$	$y$	$=$	$-$	$8$
$+$		$2$	$x$	$+$	$3$	$y$	$=$		$9$
						$y$	$=$		$1$

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 $x$ .

$- 2 x - 2 \cdot 1 = - 8$

Multiply $- 2$ by $1$ .

$- 2 x - 2 = - 8$

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

Add $2$ to both sides of the equation.

$- 2 x = - 8 + 2$

Add $- 8$ and $2$ .

$- 2 x = - 6$

Divide each term in $- 2 x = - 6$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 6$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 6}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 2}$

Simplify the right side.

Divide $- 6$ by $- 2$ .

$x = 3$

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

$(3, 1)$

The result can be shown in multiple forms.

Point Form:

$(3, 1)$

Equation Form:

$x = 3, y = 1$

Solve by Addition/Elimination x+y=4 2x+3y=9

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