Solve by Addition/Elimination 5x+y=8 2x-3y=10

$5 x + y = 8$ $2 x - 3 y = 10$

Step 1

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

$(3) \cdot (5 x + y) = (3) (8)$

$2 x - 3 y = 10$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$3 (5 x) + 3 y = (3) (8)$

$2 x - 3 y = 10$

Multiply $5$ by $3$ .

$15 x + 3 y = (3) (8)$

$2 x - 3 y = 10$

$15 x + 3 y = (3) (8)$

$2 x - 3 y = 10$

$15 x + 3 y = (3) (8)$

$2 x - 3 y = 10$

Simplify the right side.

Multiply $3$ by $8$ .

$15 x + 3 y = 24$

$2 x - 3 y = 10$

$15 x + 3 y = 24$

$2 x - 3 y = 10$

$15 x + 3 y = 24$

$2 x - 3 y = 10$

Step 3

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

	$1$	$5$	$x$	$+$	$3$	$y$	$=$	$2$	$4$
$+$		$2$	$x$	$-$	$3$	$y$	$=$	$1$	$0$
	$1$	$7$	$x$				$=$	$3$	$4$

Step 4

Divide each term in $17 x = 34$ by $17$ and simplify.

Divide each term in $17 x = 34$ by $17$ .

$\frac{17 x}{17} = \frac{34}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 x}{17} = \frac{34}{17}$

Divide $x$ by $1$ .

$x = \frac{34}{17}$

Simplify the right side.

Divide $34$ by $17$ .

$x = 2$

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 $y$ .

$15 (2) + 3 y = 24$

Multiply $15$ by $2$ .

$30 + 3 y = 24$

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

Subtract $30$ from both sides of the equation.

$3 y = 24 - 30$

Subtract $30$ from $24$ .

$3 y = - 6$

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

Divide each term in $3 y = - 6$ by $3$ .

$\frac{3 y}{3} = \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 6}{3}$

Divide $y$ by $1$ .

$y = \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$y = - 2$

Step 6

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

$(2, - 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, - 2)$

Equation Form:

$x = 2, y = - 2$

Step 8

Solve by Addition/Elimination 5x+y=8 2x-3y=10

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