Solve by Addition/Elimination 4x-y=-4 5x=2y+1

$4 x - y = - 4$ $5 x = 2 y + 1$

Step 1

Subtract $2 y$ from both sides of the equation.

$5 x - 2 y = 1$

$4 x - y = - 4$

Step 2

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

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

$5 x - 2 y = 1$

Step 3

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$5 x - 2 y = 1$

Multiply.

Multiply $4$ by $- 2$ .

$- 8 x - 2 (- y) = (- 2) (- 4)$

$5 x - 2 y = 1$

Multiply $- 1$ by $- 2$ .

$- 8 x + 2 y = (- 2) (- 4)$

$5 x - 2 y = 1$

$- 8 x + 2 y = (- 2) (- 4)$

$5 x - 2 y = 1$

$- 8 x + 2 y = (- 2) (- 4)$

$5 x - 2 y = 1$

$- 8 x + 2 y = (- 2) (- 4)$

$5 x - 2 y = 1$

Simplify the right side.

Multiply $- 2$ by $- 4$ .

$- 8 x + 2 y = 8$

$5 x - 2 y = 1$

$- 8 x + 2 y = 8$

$5 x - 2 y = 1$

$- 8 x + 2 y = 8$

$5 x - 2 y = 1$

Step 4

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

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

Step 5

Divide each term in $- 3 x = 9$ by $- 3$ and simplify.

Divide each term in $- 3 x = 9$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{9}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{9}{- 3}$

Divide $x$ by $1$ .

$x = \frac{9}{- 3}$

Simplify the right side.

Divide $9$ by $- 3$ .

$x = - 3$

Step 6

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 $y$ .

$- 8 \cdot - 3 + 2 y = 8$

Multiply $- 8$ by $- 3$ .

$24 + 2 y = 8$

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

Subtract $24$ from both sides of the equation.

$2 y = 8 - 24$

Subtract $24$ from $8$ .

$2 y = - 16$

Divide each term in $2 y = - 16$ by $2$ and simplify.

Divide each term in $2 y = - 16$ by $2$ .

$\frac{2 y}{2} = \frac{- 16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 16}{2}$

Divide $y$ by $1$ .

$y = \frac{- 16}{2}$

Simplify the right side.

Divide $- 16$ by $2$ .

$y = - 8$

Step 7

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

$(- 3, - 8)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 3, - 8)$

Equation Form:

$x = - 3, y = - 8$

Step 9

Solve by Addition/Elimination 4x-y=-4 5x=2y+1

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