Solve by Addition/Elimination 12x-5y=30 y=2x-6

$12 x - 5 y = 30$ $y = 2 x - 6$

Step 1

Subtract $2 x$ from both sides of the equation.

$12 x - 5 y = 30, y - 2 x = - 6$

Step 2

Reorder the polynomial.

$- 2 x + y = - 6$

$12 x - 5 y = 30$

Step 3

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

$12 x - 5 y = 30$

$(5) \cdot (- 2 x + y) = (5) (- 6)$

Step 4

Simplify.

Simplify the left side.

Simplify $(5) \cdot (- 2 x + y)$ .

Apply the distributive property.

$12 x - 5 y = 30$

$5 (- 2 x) + 5 y = (5) (- 6)$

Multiply $- 2$ by $5$ .

$12 x - 5 y = 30$

$- 10 x + 5 y = (5) (- 6)$

$12 x - 5 y = 30$

$- 10 x + 5 y = (5) (- 6)$

$12 x - 5 y = 30$

$- 10 x + 5 y = (5) (- 6)$

Simplify the right side.

Multiply $5$ by $- 6$ .

$12 x - 5 y = 30$

$- 10 x + 5 y = - 30$

$12 x - 5 y = 30$

$- 10 x + 5 y = - 30$

$12 x - 5 y = 30$

$- 10 x + 5 y = - 30$

Step 5

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

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

Step 6

Divide each term in $2 x = 0$ by $2$ and simplify.

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x = 0$

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 $y$ .

$12 (0) - 5 y = 30$

Simplify $12 (0) - 5 y$ .

Multiply $12$ by $0$ .

$0 - 5 y = 30$

Subtract $5 y$ from $0$ .

$- 5 y = 30$

Divide each term in $- 5 y = 30$ by $- 5$ and simplify.

Divide each term in $- 5 y = 30$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{30}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{30}{- 5}$

Divide $y$ by $1$ .

$y = \frac{30}{- 5}$

Simplify the right side.

Divide $30$ by $- 5$ .

$y = - 6$

Step 8

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

$(0, - 6)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(0, - 6)$

Equation Form:

$x = 0, y = - 6$

Step 10

Solve by Addition/Elimination 12x-5y=30 y=2x-6

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