Solve by Addition/Elimination 13x+2y=1 5x-2y=-19

$13 x + 2 y = 1$ $5 x - 2 y = - 19$

Step 1

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

	$1$	$3$	$x$	$+$	$2$	$y$	$=$			$1$
$+$		$5$	$x$	$-$	$2$	$y$	$=$	$-$	$1$	$9$
	$1$	$8$	$x$				$=$	$-$	$1$	$8$

Step 2

Divide each term in $18 x = - 18$ by $18$ and simplify.

Divide each term in $18 x = - 18$ by $18$ .

$\frac{18 x}{18} = \frac{- 18}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 x}{18} = \frac{- 18}{18}$

Divide $x$ by $1$ .

$x = \frac{- 18}{18}$

Simplify the right side.

Divide $- 18$ by $18$ .

$x = - 1$

Step 3

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 $y$ .

$13 (- 1) + 2 y = 1$

Multiply $13$ by $- 1$ .

$- 13 + 2 y = 1$

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

Add $13$ to both sides of the equation.

$2 y = 1 + 13$

Add $1$ and $13$ .

$2 y = 14$

Divide each term in $2 y = 14$ by $2$ and simplify.

Divide each term in $2 y = 14$ by $2$ .

$\frac{2 y}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{14}{2}$

Divide $y$ by $1$ .

$y = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$y = 7$

Step 4

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

$(- 1, 7)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 1, 7)$

Equation Form:

$x = - 1, y = 7$

Step 6

Solve by Addition/Elimination 13x+2y=1 5x-2y=-19

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