Solve by Addition/Elimination 4y+x=-17 -2y+2x=16

$4 y + x = - 17$ $- 2 y + 2 x = 16$

Step 1

Simplify the left side.

Reorder $4 y$ and $x$ .

$x + 4 y = - 17$

$- 2 y + 2 x = 16$

$x + 4 y = - 17$

$- 2 y + 2 x = 16$

Step 2

Simplify the left side.

Reorder $- 2 y$ and $2 x$ .

$2 x - 2 y = 16$

$x + 4 y = - 17$

$2 x - 2 y = 16$

$x + 4 y = - 17$

Step 3

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

$(- 2) \cdot (x + 4 y) = (- 2) (- 17)$

$2 x - 2 y = 16$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (x + 4 y)$ .

Apply the distributive property.

$- 2 x - 2 (4 y) = (- 2) (- 17)$

$2 x - 2 y = 16$

Multiply $4$ by $- 2$ .

$- 2 x - 8 y = (- 2) (- 17)$

$2 x - 2 y = 16$

$- 2 x - 8 y = (- 2) (- 17)$

$2 x - 2 y = 16$

$- 2 x - 8 y = (- 2) (- 17)$

$2 x - 2 y = 16$

Simplify the right side.

Multiply $- 2$ by $- 17$ .

$- 2 x - 8 y = 34$

$2 x - 2 y = 16$

$- 2 x - 8 y = 34$

$2 x - 2 y = 16$

$- 2 x - 8 y = 34$

$2 x - 2 y = 16$

Step 5

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

	$-$	$2$	$x$		$-$	$8$	$y$	$=$	$3$	$4$
$+$		$2$	$x$		$-$	$2$	$y$	$=$	$1$	$6$
				$-$	$1$	$0$	$y$	$=$	$5$	$0$

Step 6

Divide each term in $- 10 y = 50$ by $- 10$ and simplify.

Divide each term in $- 10 y = 50$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{50}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{50}{- 10}$

Divide $y$ by $1$ .

$y = \frac{50}{- 10}$

Simplify the right side.

Divide $50$ by $- 10$ .

$y = - 5$

Step 7

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 $x$ .

$- 2 x - 8 \cdot - 5 = 34$

Multiply $- 8$ by $- 5$ .

$- 2 x + 40 = 34$

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

Subtract $40$ from both sides of the equation.

$- 2 x = 34 - 40$

Subtract $40$ from $34$ .

$- 2 x = - 6$

Divide each term in $- 2 x = - 6$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 6$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 6}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 2}$

Simplify the right side.

Divide $- 6$ by $- 2$ .

$x = 3$

Step 8

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

$(3, - 5)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(3, - 5)$

Equation Form:

$x = 3, y = - 5$

Step 10

Solve by Addition/Elimination 4y+x=-17 -2y+2x=16

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