Solve by Addition/Elimination 3x+2y=12 , 6x+3y=21

$3 x + 2 y = 12$ , $6 x + 3 y = 21$

Step 1

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

$(- 2) \cdot (3 x + 2 y) = (- 2) (12)$

$6 x + 3 y = 21$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (3 x + 2 y)$ .

Apply the distributive property.

$- 2 (3 x) - 2 (2 y) = (- 2) (12)$

$6 x + 3 y = 21$

Multiply.

Multiply $3$ by $- 2$ .

$- 6 x - 2 (2 y) = (- 2) (12)$

$6 x + 3 y = 21$

Multiply $2$ by $- 2$ .

$- 6 x - 4 y = (- 2) (12)$

$6 x + 3 y = 21$

$- 6 x - 4 y = (- 2) (12)$

$6 x + 3 y = 21$

$- 6 x - 4 y = (- 2) (12)$

$6 x + 3 y = 21$

$- 6 x - 4 y = (- 2) (12)$

$6 x + 3 y = 21$

Simplify the right side.

Multiply $- 2$ by $12$ .

$- 6 x - 4 y = - 24$

$6 x + 3 y = 21$

$- 6 x - 4 y = - 24$

$6 x + 3 y = 21$

$- 6 x - 4 y = - 24$

$6 x + 3 y = 21$

Step 3

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

	$-$	$6$	$x$	$-$	$4$	$y$	$=$	$-$	$2$	$4$
$+$		$6$	$x$	$+$	$3$	$y$	$=$		$2$	$1$
					$-$	$y$	$=$		$-$	$3$

Step 4

Divide each term in $- y = - 3$ by $- 1$ and simplify.

Divide each term in $- y = - 3$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 3}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$y = 3$

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 $x$ .

$- 6 x - 4 \cdot 3 = - 24$

Multiply $- 4$ by $3$ .

$- 6 x - 12 = - 24$

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

Add $12$ to both sides of the equation.

$- 6 x = - 24 + 12$

Add $- 24$ and $12$ .

$- 6 x = - 12$

Divide each term in $- 6 x = - 12$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 12$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 12}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 6}$

Simplify the right side.

Divide $- 12$ by $- 6$ .

$x = 2$

Step 6

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

$(2, 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$

Step 8

Solve by Addition/Elimination 3x+2y=12 , 6x+3y=21

Related Questions

Support LCMGCF.com by disabling your adblocker.