Solve by Addition/Elimination -9y+4x-20=0 , -7y+16x-80=0

$- 9 y + 4 x - 20 = 0$ , $- 7 y + 16 x - 80 = 0$

Step 1

Simplify the left side.

Reorder $- 9 y$ and $4 x$ .

$4 x - 9 y - 20 = 0$

$- 7 y + 16 x - 80 = 0$

$4 x - 9 y - 20 = 0$

$- 7 y + 16 x - 80 = 0$

Step 2

Simplify the left side.

Reorder $- 7 y$ and $16 x$ .

$16 x - 7 y - 80 = 0$

$4 x - 9 y - 20 = 0$

$16 x - 7 y - 80 = 0$

$4 x - 9 y - 20 = 0$

Step 3

Add $20$ to both sides of the equation.

$4 x - 9 y = 20$

$16 x - 7 y - 80 = 0$

Step 4

Add $80$ to both sides of the equation.

$16 x - 7 y = 80$

$4 x - 9 y = 20$

Step 5

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

$(- 4) \cdot (4 x - 9 y) = (- 4) (20)$

$16 x - 7 y = 80$

Step 6

Simplify.

Simplify the left side.

Simplify $(- 4) \cdot (4 x - 9 y)$ .

Apply the distributive property.

$- 4 (4 x) - 4 (- 9 y) = (- 4) (20)$

$16 x - 7 y = 80$

Multiply.

Multiply $4$ by $- 4$ .

$- 16 x - 4 (- 9 y) = (- 4) (20)$

$16 x - 7 y = 80$

Multiply $- 9$ by $- 4$ .

$- 16 x + 36 y = (- 4) (20)$

$16 x - 7 y = 80$

$- 16 x + 36 y = (- 4) (20)$

$16 x - 7 y = 80$

$- 16 x + 36 y = (- 4) (20)$

$16 x - 7 y = 80$

$- 16 x + 36 y = (- 4) (20)$

$16 x - 7 y = 80$

Simplify the right side.

Multiply $- 4$ by $20$ .

$- 16 x + 36 y = - 80$

$16 x - 7 y = 80$

$- 16 x + 36 y = - 80$

$16 x - 7 y = 80$

$- 16 x + 36 y = - 80$

$16 x - 7 y = 80$

Step 7

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

	$-$	$1$	$6$	$x$	$+$	$3$	$6$	$y$	$=$	$-$	$8$	$0$
$+$		$1$	$6$	$x$		$-$	$7$	$y$	$=$		$8$	$0$
						$2$	$9$	$y$	$=$			$0$

Step 8

Divide each term in $29 y = 0$ by $29$ and simplify.

Divide each term in $29 y = 0$ by $29$ .

$\frac{29 y}{29} = \frac{0}{29}$

Simplify the left side.

Cancel the common factor of $29$ .

Cancel the common factor.

$\frac{29 y}{29} = \frac{0}{29}$

Divide $y$ by $1$ .

$y = \frac{0}{29}$

Simplify the right side.

Divide $0$ by $29$ .

$y = 0$

Step 9

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 $x$ .

$- 16 x + 36 (0) = - 80$

Simplify $- 16 x + 36 (0)$ .

Multiply $36$ by $0$ .

$- 16 x + 0 = - 80$

Add $- 16 x$ and $0$ .

$- 16 x = - 80$

Divide each term in $- 16 x = - 80$ by $- 16$ and simplify.

Divide each term in $- 16 x = - 80$ by $- 16$ .

$\frac{- 16 x}{- 16} = \frac{- 80}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 x}{- 16} = \frac{- 80}{- 16}$

Divide $x$ by $1$ .

$x = \frac{- 80}{- 16}$

Simplify the right side.

Divide $- 80$ by $- 16$ .

$x = 5$

Step 10

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

$(5, 0)$

Step 11

The result can be shown in multiple forms.

Point Form:

$(5, 0)$

Equation Form:

$x = 5, y = 0$

Step 12

Solve by Addition/Elimination -9y+4x-20=0 , -7y+16x-80=0

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