Solve by Addition/Elimination 5x+2y=5 3x-y=14

$5 x + 2 y = 5$ $3 x - y = 14$

Step 1

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

$5 x + 2 y = 5$

$(2) \cdot (3 x - y) = (2) (14)$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (3 x - y)$ .

Apply the distributive property.

$5 x + 2 y = 5$

$2 (3 x) + 2 (- y) = (2) (14)$

Multiply.

Multiply $3$ by $2$ .

$5 x + 2 y = 5$

$6 x + 2 (- y) = (2) (14)$

Multiply $- 1$ by $2$ .

$5 x + 2 y = 5$

$6 x - 2 y = (2) (14)$

$5 x + 2 y = 5$

$6 x - 2 y = (2) (14)$

$5 x + 2 y = 5$

$6 x - 2 y = (2) (14)$

$5 x + 2 y = 5$

$6 x - 2 y = (2) (14)$

Simplify the right side.

Multiply $2$ by $14$ .

$5 x + 2 y = 5$

$6 x - 2 y = 28$

$5 x + 2 y = 5$

$6 x - 2 y = 28$

$5 x + 2 y = 5$

$6 x - 2 y = 28$

Step 3

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

		$5$	$x$	$+$	$2$	$y$	$=$		$5$
$+$		$6$	$x$	$-$	$2$	$y$	$=$	$2$	$8$
	$1$	$1$	$x$				$=$	$3$	$3$

Step 4

Divide each term in $11 x = 33$ by $11$ and simplify.

Divide each term in $11 x = 33$ by $11$ .

$\frac{11 x}{11} = \frac{33}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{33}{11}$

Divide $x$ by $1$ .

$x = \frac{33}{11}$

Simplify the right side.

Divide $33$ by $11$ .

$x = 3$

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 $y$ .

$5 (3) + 2 y = 5$

Multiply $5$ by $3$ .

$15 + 2 y = 5$

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

Subtract $15$ from both sides of the equation.

$2 y = 5 - 15$

Subtract $15$ from $5$ .

$2 y = - 10$

Divide each term in $2 y = - 10$ by $2$ and simplify.

Divide each term in $2 y = - 10$ by $2$ .

$\frac{2 y}{2} = \frac{- 10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 10}{2}$

Divide $y$ by $1$ .

$y = \frac{- 10}{2}$

Simplify the right side.

Divide $- 10$ by $2$ .

$y = - 5$

Step 6

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

$(3, - 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(3, - 5)$

Equation Form:

$x = 3, y = - 5$

Step 8

Solve by Addition/Elimination 5x+2y=5 3x-y=14

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