Solve by Addition/Elimination 5x+3y=31 , 2x+3y=25

$5 x + 3 y = 31$ , $2 x + 3 y = 25$

Step 1

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

$(- 1) \cdot (5 x + 3 y) = (- 1) (31)$

$2 x + 3 y = 25$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (5 x + 3 y)$ .

Apply the distributive property.

$- 1 (5 x) - 1 (3 y) = (- 1) (31)$

$2 x + 3 y = 25$

Multiply.

Multiply $5$ by $- 1$ .

$- 5 x - 1 (3 y) = (- 1) (31)$

$2 x + 3 y = 25$

Multiply $3$ by $- 1$ .

$- 5 x - 3 y = (- 1) (31)$

$2 x + 3 y = 25$

$- 5 x - 3 y = (- 1) (31)$

$2 x + 3 y = 25$

$- 5 x - 3 y = (- 1) (31)$

$2 x + 3 y = 25$

$- 5 x - 3 y = (- 1) (31)$

$2 x + 3 y = 25$

Simplify the right side.

Multiply $- 1$ by $31$ .

$- 5 x - 3 y = - 31$

$2 x + 3 y = 25$

$- 5 x - 3 y = - 31$

$2 x + 3 y = 25$

$- 5 x - 3 y = - 31$

$2 x + 3 y = 25$

Step 3

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

	$-$	$5$	$x$	$-$	$3$	$y$	$=$	$-$	$3$	$1$
$+$		$2$	$x$	$+$	$3$	$y$	$=$		$2$	$5$
	$-$	$3$	$x$				$=$		$-$	$6$

Step 4

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 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 $y$ .

$- 5 \cdot 2 - 3 y = - 31$

Multiply $- 5$ by $2$ .

$- 10 - 3 y = - 31$

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

Add $10$ to both sides of the equation.

$- 3 y = - 31 + 10$

Add $- 31$ and $10$ .

$- 3 y = - 21$

Divide each term in $- 3 y = - 21$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 21$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 21}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 21}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 21}{- 3}$

Simplify the right side.

Divide $- 21$ by $- 3$ .

$y = 7$

Step 6

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

$(2, 7)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, 7)$

Equation Form:

$x = 2, y = 7$

Step 8

Solve by Addition/Elimination 5x+3y=31 , 2x+3y=25

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