Solve by Addition/Elimination 3x+6y=24 y=3/2x-4

$3 x + 6 y = 24$ $y = \frac{3}{2} x - 4$

Step 1

Multiply each term in $y = \frac{3}{2} x - 4$ by $2$ to eliminate the fractions.

Multiply each term in $y = \frac{3}{2} x - 4$ by $2$ .

$y \cdot 2 = \frac{3}{2} x \cdot 2 - 4 \cdot 2$

$3 x + 6 y = 24$

Simplify the left side.

Move $2$ to the left of $y$ .

$2 y = \frac{3}{2} x \cdot 2 - 4 \cdot 2$

$3 x + 6 y = 24$

$2 y = \frac{3}{2} x \cdot 2 - 4 \cdot 2$

$3 x + 6 y = 24$

Simplify the right side.

Simplify each term.

Combine $\frac{3}{2}$ and $x$ .

$2 y = \frac{3 x}{2} \cdot 2 - 4 \cdot 2$

$3 x + 6 y = 24$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 y = \frac{3 x}{2} \cdot 2 - 4 \cdot 2$

$3 x + 6 y = 24$

Rewrite the expression.

$2 y = 3 x - 4 \cdot 2$

$3 x + 6 y = 24$

$2 y = 3 x - 4 \cdot 2$

$3 x + 6 y = 24$

Multiply $- 4$ by $2$ .

$2 y = 3 x - 8$

$3 x + 6 y = 24$

$2 y = 3 x - 8$

$3 x + 6 y = 24$

$2 y = 3 x - 8$

$3 x + 6 y = 24$

$2 y = 3 x - 8$

$3 x + 6 y = 24$

Step 2

Move all terms containing variables to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$2 y - 3 x = - 8$

$3 x + 6 y = 24$

Reorder $2 y$ and $- 3 x$ .

$- 3 x + 2 y = - 8$

$3 x + 6 y = 24$

$- 3 x + 2 y = - 8$

$3 x + 6 y = 24$

Step 3

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

		$3$	$x$	$+$	$6$	$y$	$=$	$2$	$4$
$+$	$-$	$3$	$x$	$+$	$2$	$y$	$=$	$-$	$8$
					$8$	$y$	$=$	$1$	$6$

Step 4

Divide each term in $8 y = 16$ by $8$ and simplify.

Divide each term in $8 y = 16$ by $8$ .

$\frac{8 y}{8} = \frac{16}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{16}{8}$

Divide $y$ by $1$ .

$y = \frac{16}{8}$

Simplify the right side.

Divide $16$ by $8$ .

$y = 2$

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 $x$ .

$3 x + 6 (2) = 24$

Multiply $6$ by $2$ .

$3 x + 12 = 24$

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

Subtract $12$ from both sides of the equation.

$3 x = 24 - 12$

Subtract $12$ from $24$ .

$3 x = 12$

Divide each term in $3 x = 12$ by $3$ and simplify.

Divide each term in $3 x = 12$ by $3$ .

$\frac{3 x}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{12}{3}$

Divide $x$ by $1$ .

$x = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$x = 4$

Step 6

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

$(4, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, 2)$

Equation Form:

$x = 4, y = 2$

Step 8

Solve by Addition/Elimination 3x+6y=24 y=3/2x-4

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