Solve by Addition/Elimination 2x-8y=6 , 3x-12y=9

$2 x - 8 y = 6$ , $3 x - 12 y = 9$

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

$(- 3) \cdot (2 x - 8 y) = (- 3) (6)$

$(2) \cdot (3 x - 12 y) = (2) (9)$

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (2 x - 8 y)$ .

Apply the distributive property.

$- 3 (2 x) - 3 (- 8 y) = (- 3) (6)$

$(2) \cdot (3 x - 12 y) = (2) (9)$

Multiply.

Multiply $2$ by $- 3$ .

$- 6 x - 3 (- 8 y) = (- 3) (6)$

$(2) \cdot (3 x - 12 y) = (2) (9)$

Multiply $- 8$ by $- 3$ .

$- 6 x + 24 y = (- 3) (6)$

$(2) \cdot (3 x - 12 y) = (2) (9)$

$- 6 x + 24 y = (- 3) (6)$

$(2) \cdot (3 x - 12 y) = (2) (9)$

$- 6 x + 24 y = (- 3) (6)$

$(2) \cdot (3 x - 12 y) = (2) (9)$

$- 6 x + 24 y = (- 3) (6)$

$(2) \cdot (3 x - 12 y) = (2) (9)$

Simplify the right side.

Multiply $- 3$ by $6$ .

$- 6 x + 24 y = - 18$

$(2) \cdot (3 x - 12 y) = (2) (9)$

$- 6 x + 24 y = - 18$

$(2) \cdot (3 x - 12 y) = (2) (9)$

Simplify the left side.

Simplify $(2) \cdot (3 x - 12 y)$ .

Apply the distributive property.

$- 6 x + 24 y = - 18$

$2 (3 x) + 2 (- 12 y) = (2) (9)$

Multiply.

Multiply $3$ by $2$ .

$- 6 x + 24 y = - 18$

$6 x + 2 (- 12 y) = (2) (9)$

Multiply $- 12$ by $2$ .

$- 6 x + 24 y = - 18$

$6 x - 24 y = (2) (9)$

$- 6 x + 24 y = - 18$

$6 x - 24 y = (2) (9)$

$- 6 x + 24 y = - 18$

$6 x - 24 y = (2) (9)$

$- 6 x + 24 y = - 18$

$6 x - 24 y = (2) (9)$

Simplify the right side.

Multiply $2$ by $9$ .

$- 6 x + 24 y = - 18$

$6 x - 24 y = 18$

$- 6 x + 24 y = - 18$

$6 x - 24 y = 18$

$- 6 x + 24 y = - 18$

$6 x - 24 y = 18$

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

	$-$	$6$	$x$	$+$	$2$	$4$	$y$	$=$	$-$	$1$	$8$
$+$		$6$	$x$	$-$	$2$	$4$	$y$	$=$		$1$	$8$
							$0$	$=$			$0$

Since $0 = 0$ , the equations intersect at an infinite number of points.

Infinite number of solutions

Solve one of the equations for $y$ .

Add $6 x$ to both sides of the equation.

$24 y = - 18 + 6 x$

Divide each term in $24 y = - 18 + 6 x$ by $24$ and simplify.

Divide each term in $24 y = - 18 + 6 x$ by $24$ .

$\frac{24 y}{24} = \frac{- 18}{24} + \frac{6 x}{24}$

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{24 y}{24} = \frac{- 18}{24} + \frac{6 x}{24}$

Divide $y$ by $1$ .

$y = \frac{- 18}{24} + \frac{6 x}{24}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 18$ and $24$ .

Factor $6$ out of $- 18$ .

$y = \frac{6 (- 3)}{24} + \frac{6 x}{24}$

Cancel the common factors.

Factor $6$ out of $24$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Cancel the common factor of $6$ and $24$ .

Factor $6$ out of $6 x$ .

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

Cancel the common factors.

Factor $6$ out of $24$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

The solution is the set of ordered pairs that make $y = - \frac{3}{4} + \frac{x}{4}$ true.

$(x, - \frac{3}{4} + \frac{x}{4})$

The result can be shown in multiple forms.

Point Form:

$(x, - \frac{3}{4} + \frac{x}{4})$

Equation Form:

$x = x, y = - \frac{3}{4} + \frac{x}{4}$

Solve by Addition/Elimination 2x-8y=6 , 3x-12y=9

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