Solve by Addition/Elimination -5x-3y-9=0 4x-18y-54=0

$- 5 x - 3 y - 9 = 0$ $4 x - 18 y - 54 = 0$

Step 1

Add $9$ to both sides of the equation.

$- 5 x - 3 y = 9$

$4 x - 18 y - 54 = 0$

Step 2

Add $54$ to both sides of the equation.

$4 x - 18 y = 54$

$- 5 x - 3 y = 9$

Step 3

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

$(- 6) \cdot (- 5 x - 3 y) = (- 6) (9)$

$4 x - 18 y = 54$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 6) \cdot (- 5 x - 3 y)$ .

Apply the distributive property.

$- 6 (- 5 x) - 6 (- 3 y) = (- 6) (9)$

$4 x - 18 y = 54$

Multiply.

Multiply $- 5$ by $- 6$ .

$30 x - 6 (- 3 y) = (- 6) (9)$

$4 x - 18 y = 54$

Multiply $- 3$ by $- 6$ .

$30 x + 18 y = (- 6) (9)$

$4 x - 18 y = 54$

$30 x + 18 y = (- 6) (9)$

$4 x - 18 y = 54$

$30 x + 18 y = (- 6) (9)$

$4 x - 18 y = 54$

$30 x + 18 y = (- 6) (9)$

$4 x - 18 y = 54$

Simplify the right side.

Multiply $- 6$ by $9$ .

$30 x + 18 y = - 54$

$4 x - 18 y = 54$

$30 x + 18 y = - 54$

$4 x - 18 y = 54$

$30 x + 18 y = - 54$

$4 x - 18 y = 54$

Step 5

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

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

Step 6

Divide each term in $34 x = 0$ by $34$ and simplify.

Divide each term in $34 x = 0$ by $34$ .

$\frac{34 x}{34} = \frac{0}{34}$

Simplify the left side.

Cancel the common factor of $34$ .

Cancel the common factor.

$\frac{34 x}{34} = \frac{0}{34}$

Divide $x$ by $1$ .

$x = \frac{0}{34}$

Simplify the right side.

Divide $0$ by $34$ .

$x = 0$

Step 7

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 $y$ .

$30 (0) + 18 y = - 54$

Simplify $30 (0) + 18 y$ .

Multiply $30$ by $0$ .

$0 + 18 y = - 54$

Add $0$ and $18 y$ .

$18 y = - 54$

Divide each term in $18 y = - 54$ by $18$ and simplify.

Divide each term in $18 y = - 54$ by $18$ .

$\frac{18 y}{18} = \frac{- 54}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 y}{18} = \frac{- 54}{18}$

Divide $y$ by $1$ .

$y = \frac{- 54}{18}$

Simplify the right side.

Divide $- 54$ by $18$ .

$y = - 3$

Step 8

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

$(0, - 3)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(0, - 3)$

Equation Form:

$x = 0, y = - 3$

Step 10

Solve by Addition/Elimination -5x-3y-9=0 4x-18y-54=0

Related Questions

Support LCMGCF.com by disabling your adblocker.