Solve by Addition/Elimination x-y=11 2x+y=19

$x - y = 11$ $2 x + y = 19$

Step 1

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

		$x$	$-$	$y$	$=$	$1$	$1$
$+$	$2$	$x$	$+$	$y$	$=$	$1$	$9$
	$3$	$x$			$=$	$3$	$0$

Step 2

Divide each term in $3 x = 30$ by $3$ and simplify.

Divide each term in $3 x = 30$ by $3$ .

$\frac{3 x}{3} = \frac{30}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{30}{3}$

Divide $x$ by $1$ .

$x = \frac{30}{3}$

Simplify the right side.

Divide $30$ by $3$ .

$x = 10$

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 $y$ .

$(10) - y = 11$

Remove parentheses.

$10 - y = 11$

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

Subtract $10$ from both sides of the equation.

$- y = 11 - 10$

Subtract $10$ from $11$ .

$- y = 1$

Divide each term in $- y = 1$ by $- 1$ and simplify.

Divide each term in $- y = 1$ by $- 1$ .

$\frac{- y}{- 1} = \frac{1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{1}{- 1}$

Divide $y$ by $1$ .

$y = \frac{1}{- 1}$

Simplify the right side.

Divide $1$ by $- 1$ .

$y = - 1$

Step 4

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

$(10, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(10, - 1)$

Equation Form:

$x = 10, y = - 1$

Step 6

Solve by Addition/Elimination x-y=11 2x+y=19

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