Solve by Addition/Elimination 2x+3y=9 , x+5y=8

$2 x + 3 y = 9$ , $x + 5 y = 8$

Step 1

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

$2 x + 3 y = 9$

$(- 2) \cdot (x + 5 y) = (- 2) (8)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$2 x + 3 y = 9$

$- 2 x - 2 (5 y) = (- 2) (8)$

Multiply $5$ by $- 2$ .

$2 x + 3 y = 9$

$- 2 x - 10 y = (- 2) (8)$

$2 x + 3 y = 9$

$- 2 x - 10 y = (- 2) (8)$

$2 x + 3 y = 9$

$- 2 x - 10 y = (- 2) (8)$

Simplify the right side.

Multiply $- 2$ by $8$ .

$2 x + 3 y = 9$

$- 2 x - 10 y = - 16$

$2 x + 3 y = 9$

$- 2 x - 10 y = - 16$

$2 x + 3 y = 9$

$- 2 x - 10 y = - 16$

Step 3

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

		$2$	$x$	$+$		$3$	$y$	$=$			$9$
$+$	$-$	$2$	$x$	$-$	$1$	$0$	$y$	$=$	$-$	$1$	$6$
					$-$	$7$	$y$	$=$		$-$	$7$

Step 4

Divide each term in $- 7 y = - 7$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 7$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 7}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 7}{- 7}$

Divide $y$ by $1$ .

$y = \frac{- 7}{- 7}$

Simplify the right side.

Divide $- 7$ by $- 7$ .

$y = 1$

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 $x$ .

$2 x + 3 (1) = 9$

Multiply $3$ by $1$ .

$2 x + 3 = 9$

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

Subtract $3$ from both sides of the equation.

$2 x = 9 - 3$

Subtract $3$ from $9$ .

$2 x = 6$

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 $2$ .

$x = 3$

Step 6

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

$(3, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(3, 1)$

Equation Form:

$x = 3, y = 1$

Step 8

Solve by Addition/Elimination 2x+3y=9 , x+5y=8

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