Solve by Addition/Elimination 3x+2y=8 x+5y=7

$3 x + 2 y = 8$ $x + 5 y = 7$

Step 1

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

$3 x + 2 y = 8$

$(- 3) \cdot (x + 5 y) = (- 3) (7)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (x + 5 y)$ .

Apply the distributive property.

$3 x + 2 y = 8$

$- 3 x - 3 (5 y) = (- 3) (7)$

Multiply $5$ by $- 3$ .

$3 x + 2 y = 8$

$- 3 x - 15 y = (- 3) (7)$

$3 x + 2 y = 8$

$- 3 x - 15 y = (- 3) (7)$

$3 x + 2 y = 8$

$- 3 x - 15 y = (- 3) (7)$

Simplify the right side.

Multiply $- 3$ by $7$ .

$3 x + 2 y = 8$

$- 3 x - 15 y = - 21$

$3 x + 2 y = 8$

$- 3 x - 15 y = - 21$

$3 x + 2 y = 8$

$- 3 x - 15 y = - 21$

Step 3

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

		$3$	$x$	$+$		$2$	$y$	$=$			$8$
$+$	$-$	$3$	$x$	$-$	$1$	$5$	$y$	$=$	$-$	$2$	$1$
				$-$	$1$	$3$	$y$	$=$	$-$	$1$	$3$

Step 4

Divide each term in $- 13 y = - 13$ by $- 13$ and simplify.

Divide each term in $- 13 y = - 13$ by $- 13$ .

$\frac{- 13 y}{- 13} = \frac{- 13}{- 13}$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 y}{- 13} = \frac{- 13}{- 13}$

Divide $y$ by $1$ .

$y = \frac{- 13}{- 13}$

Simplify the right side.

Divide $- 13$ by $- 13$ .

$y = 1$

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 $x$ .

$3 x + 2 (1) = 8$

Multiply $2$ by $1$ .

$3 x + 2 = 8$

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

Subtract $2$ from both sides of the equation.

$3 x = 8 - 2$

Subtract $2$ from $8$ .

$3 x = 6$

Divide each term in $3 x = 6$ by $3$ and simplify.

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

Step 6

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

$(2, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

Step 8

Solve by Addition/Elimination 3x+2y=8 x+5y=7

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