Solve by Addition/Elimination 5x+3y=30 3x+3y=18

$5 x + 3 y = 30$ $3 x + 3 y = 18$

Step 1

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

$(- 1) \cdot (5 x + 3 y) = (- 1) (30)$

$3 x + 3 y = 18$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (5 x + 3 y)$ .

Apply the distributive property.

$- 1 (5 x) - 1 (3 y) = (- 1) (30)$

$3 x + 3 y = 18$

Multiply.

Multiply $5$ by $- 1$ .

$- 5 x - 1 (3 y) = (- 1) (30)$

$3 x + 3 y = 18$

Multiply $3$ by $- 1$ .

$- 5 x - 3 y = (- 1) (30)$

$3 x + 3 y = 18$

$- 5 x - 3 y = (- 1) (30)$

$3 x + 3 y = 18$

$- 5 x - 3 y = (- 1) (30)$

$3 x + 3 y = 18$

$- 5 x - 3 y = (- 1) (30)$

$3 x + 3 y = 18$

Simplify the right side.

Multiply $- 1$ by $30$ .

$- 5 x - 3 y = - 30$

$3 x + 3 y = 18$

$- 5 x - 3 y = - 30$

$3 x + 3 y = 18$

$- 5 x - 3 y = - 30$

$3 x + 3 y = 18$

Step 3

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

	$-$	$5$	$x$	$-$	$3$	$y$	$=$	$-$	$3$	$0$
$+$		$3$	$x$	$+$	$3$	$y$	$=$		$1$	$8$
	$-$	$2$	$x$				$=$	$-$	$1$	$2$

Step 4

Divide each term in $- 2 x = - 12$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 12$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 12}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 2}$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$x = 6$

Step 5

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 $y$ .

$- 5 \cdot 6 - 3 y = - 30$

Multiply $- 5$ by $6$ .

$- 30 - 3 y = - 30$

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

Add $30$ to both sides of the equation.

$- 3 y = - 30 + 30$

Add $- 30$ and $30$ .

$- 3 y = 0$

Divide each term in $- 3 y = 0$ by $- 3$ and simplify.

Divide each term in $- 3 y = 0$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{0}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{0}{- 3}$

Divide $y$ by $1$ .

$y = \frac{0}{- 3}$

Simplify the right side.

Divide $0$ by $- 3$ .

$y = 0$

Step 6

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

$(6, 0)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(6, 0)$

Equation Form:

$x = 6, y = 0$

Step 8

Solve by Addition/Elimination 5x+3y=30 3x+3y=18

Related Questions

Support LCMGCF.com by disabling your adblocker.