Solve by Addition/Elimination 5x+y=26 x+5y=-14

$5 x + y = 26$ $x + 5 y = - 14$

Step 1

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

$5 x + y = 26$

$(- 5) \cdot (x + 5 y) = (- 5) (- 14)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$5 x + y = 26$

$- 5 x - 5 (5 y) = (- 5) (- 14)$

Multiply $5$ by $- 5$ .

$5 x + y = 26$

$- 5 x - 25 y = (- 5) (- 14)$

$5 x + y = 26$

$- 5 x - 25 y = (- 5) (- 14)$

$5 x + y = 26$

$- 5 x - 25 y = (- 5) (- 14)$

Simplify the right side.

Multiply $- 5$ by $- 14$ .

$5 x + y = 26$

$- 5 x - 25 y = 70$

$5 x + y = 26$

$- 5 x - 25 y = 70$

$5 x + y = 26$

$- 5 x - 25 y = 70$

Step 3

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

		$5$	$x$	$+$			$y$	$=$	$2$	$6$
$+$	$-$	$5$	$x$	$-$	$2$	$5$	$y$	$=$	$7$	$0$
				$-$	$2$	$4$	$y$	$=$	$9$	$6$

Step 4

Divide each term in $- 24 y = 96$ by $- 24$ and simplify.

Divide each term in $- 24 y = 96$ by $- 24$ .

$\frac{- 24 y}{- 24} = \frac{96}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 y}{- 24} = \frac{96}{- 24}$

Divide $y$ by $1$ .

$y = \frac{96}{- 24}$

Simplify the right side.

Divide $96$ by $- 24$ .

$y = - 4$

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 $x$ .

$5 x - 4 = 26$

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

Add $4$ to both sides of the equation.

$5 x = 26 + 4$

Add $26$ and $4$ .

$5 x = 30$

Divide each term in $5 x = 30$ by $5$ and simplify.

Divide each term in $5 x = 30$ by $5$ .

$\frac{5 x}{5} = \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{30}{5}$

Divide $x$ by $1$ .

$x = \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$x = 6$

Step 6

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

$(6, - 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(6, - 4)$

Equation Form:

$x = 6, y = - 4$

Step 8

Solve by Addition/Elimination 5x+y=26 x+5y=-14

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