Solve by Addition/Elimination 4x+13y=40 , 4x+3y=-40

$4 x + 13 y = 40$ , $4 x + 3 y = - 40$

Step 1

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

$(- 1) \cdot (4 x + 13 y) = (- 1) (40)$

$4 x + 3 y = - 40$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (4 x + 13 y)$ .

Apply the distributive property.

$- 1 (4 x) - 1 (13 y) = (- 1) (40)$

$4 x + 3 y = - 40$

Multiply.

Multiply $4$ by $- 1$ .

$- 4 x - 1 (13 y) = (- 1) (40)$

$4 x + 3 y = - 40$

Multiply $13$ by $- 1$ .

$- 4 x - 13 y = (- 1) (40)$

$4 x + 3 y = - 40$

$- 4 x - 13 y = (- 1) (40)$

$4 x + 3 y = - 40$

$- 4 x - 13 y = (- 1) (40)$

$4 x + 3 y = - 40$

$- 4 x - 13 y = (- 1) (40)$

$4 x + 3 y = - 40$

Simplify the right side.

Multiply $- 1$ by $40$ .

$- 4 x - 13 y = - 40$

$4 x + 3 y = - 40$

$- 4 x - 13 y = - 40$

$4 x + 3 y = - 40$

$- 4 x - 13 y = - 40$

$4 x + 3 y = - 40$

Step 3

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

	$-$	$4$	$x$	$-$	$1$	$3$	$y$	$=$	$-$	$4$	$0$
$+$		$4$	$x$	$+$		$3$	$y$	$=$	$-$	$4$	$0$
				$-$	$1$	$0$	$y$	$=$	$-$	$8$	$0$

Step 4

Divide each term in $- 10 y = - 80$ by $- 10$ and simplify.

Divide each term in $- 10 y = - 80$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{- 80}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{- 80}{- 10}$

Divide $y$ by $1$ .

$y = \frac{- 80}{- 10}$

Simplify the right side.

Divide $- 80$ by $- 10$ .

$y = 8$

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 $x$ .

$- 4 x - 13 \cdot 8 = - 40$

Multiply $- 13$ by $8$ .

$- 4 x - 104 = - 40$

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

Add $104$ to both sides of the equation.

$- 4 x = - 40 + 104$

Add $- 40$ and $104$ .

$- 4 x = 64$

Divide each term in $- 4 x = 64$ by $- 4$ and simplify.

Divide each term in $- 4 x = 64$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{64}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{64}{- 4}$

Divide $x$ by $1$ .

$x = \frac{64}{- 4}$

Simplify the right side.

Divide $64$ by $- 4$ .

$x = - 16$

Step 6

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

$(- 16, 8)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 16, 8)$

Equation Form:

$x = - 16, y = 8$

Step 8

Solve by Addition/Elimination 4x+13y=40 , 4x+3y=-40

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