Solve by Addition/Elimination -4x-y=-18 -7x+y=-4

$- 4 x - y = - 18$ $- 7 x + y = - 4$

Step 1

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

		$-$	$4$	$x$	$-$	$y$	$=$	$-$	$1$	$8$
$+$		$-$	$7$	$x$	$+$	$y$	$=$		$-$	$4$
	$-$	$1$	$1$	$x$			$=$	$-$	$2$	$2$

Step 2

Divide each term in $- 11 x = - 22$ by $- 11$ and simplify.

Divide each term in $- 11 x = - 22$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{- 22}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{- 22}{- 11}$

Divide $x$ by $1$ .

$x = \frac{- 22}{- 11}$

Simplify the right side.

Divide $- 22$ by $- 11$ .

$x = 2$

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 $y$ .

$- 4 \cdot 2 - y = - 18$

Multiply $- 4$ by $2$ .

$- 8 - y = - 18$

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

Add $8$ to both sides of the equation.

$- y = - 18 + 8$

Add $- 18$ and $8$ .

$- y = - 10$

Divide each term in $- y = - 10$ by $- 1$ and simplify.

Divide each term in $- y = - 10$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 10}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 10}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 10}{- 1}$

Simplify the right side.

Divide $- 10$ by $- 1$ .

$y = 10$

Step 4

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

$(2, 10)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 10)$

Equation Form:

$x = 2, y = 10$

Step 6

Solve by Addition/Elimination -4x-y=-18 -7x+y=-4

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