Solve by Addition/Elimination -x+5y=-4 4x+3y=16

$- x + 5 y = - 4$ $4 x + 3 y = 16$

Step 1

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

$(4) \cdot (- x + 5 y) = (4) (- 4)$

$4 x + 3 y = 16$

Step 2

Simplify.

Simplify the left side.

Simplify $(4) \cdot (- x + 5 y)$ .

Apply the distributive property.

$4 (- x) + 4 (5 y) = (4) (- 4)$

$4 x + 3 y = 16$

Multiply.

Multiply $- 1$ by $4$ .

$- 4 x + 4 (5 y) = (4) (- 4)$

$4 x + 3 y = 16$

Multiply $5$ by $4$ .

$- 4 x + 20 y = (4) (- 4)$

$4 x + 3 y = 16$

$- 4 x + 20 y = (4) (- 4)$

$4 x + 3 y = 16$

$- 4 x + 20 y = (4) (- 4)$

$4 x + 3 y = 16$

$- 4 x + 20 y = (4) (- 4)$

$4 x + 3 y = 16$

Simplify the right side.

Multiply $4$ by $- 4$ .

$- 4 x + 20 y = - 16$

$4 x + 3 y = 16$

$- 4 x + 20 y = - 16$

$4 x + 3 y = 16$

$- 4 x + 20 y = - 16$

$4 x + 3 y = 16$

Step 3

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

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

Step 4

Divide each term in $23 y = 0$ by $23$ and simplify.

Divide each term in $23 y = 0$ by $23$ .

$\frac{23 y}{23} = \frac{0}{23}$

Simplify the left side.

Cancel the common factor of $23$ .

Cancel the common factor.

$\frac{23 y}{23} = \frac{0}{23}$

Divide $y$ by $1$ .

$y = \frac{0}{23}$

Simplify the right side.

Divide $0$ by $23$ .

$y = 0$

Step 5

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 $x$ .

$- 4 x + 20 (0) = - 16$

Simplify $- 4 x + 20 (0)$ .

Multiply $20$ by $0$ .

$- 4 x + 0 = - 16$

Add $- 4 x$ and $0$ .

$- 4 x = - 16$

Divide each term in $- 4 x = - 16$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 16$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 16}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 16}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 16}{- 4}$

Simplify the right side.

Divide $- 16$ by $- 4$ .

$x = 4$

Step 6

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

$(4, 0)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, 0)$

Equation Form:

$x = 4, y = 0$

Step 8

Solve by Addition/Elimination -x+5y=-4 4x+3y=16

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