Solve by Addition/Elimination 6x-2y=4 -9x+3y=12

$6 x - 2 y = 4$ $- 9 x + 3 y = 12$

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

$(3) \cdot (6 x - 2 y) = (3) (4)$

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

Simplify.

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Simplify $(3) \cdot (6 x - 2 y)$ .

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Apply the distributive property.

$3 (6 x) + 3 (- 2 y) = (3) (4)$

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

Multiply.

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Multiply $6$ by $3$ .

$18 x + 3 (- 2 y) = (3) (4)$

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

Multiply $- 2$ by $3$ .

$18 x - 6 y = (3) (4)$

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

$18 x - 6 y = (3) (4)$

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

$18 x - 6 y = (3) (4)$

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

Multiply $3$ by $4$ .

$18 x - 6 y = 12$

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

Simplify $(2) \cdot (- 9 x + 3 y)$ .

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Apply the distributive property.

$18 x - 6 y = 12$

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

Multiply.

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Multiply $- 9$ by $2$ .

$18 x - 6 y = 12$

$- 18 x + 2 (3 y) = (2) (12)$

Multiply $3$ by $2$ .

$18 x - 6 y = 12$

$- 18 x + 6 y = (2) (12)$

$18 x - 6 y = 12$

$- 18 x + 6 y = (2) (12)$

$18 x - 6 y = 12$

$- 18 x + 6 y = (2) (12)$

Multiply $2$ by $12$ .

$18 x - 6 y = 12$

$- 18 x + 6 y = 24$

$18 x - 6 y = 12$

$- 18 x + 6 y = 24$

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

		$1$	$8$	$x$	$-$	$6$	$y$	$=$	$1$	$2$
$+$	$-$	$1$	$8$	$x$	$+$	$6$	$y$	$=$	$2$	$4$
							$0$	$=$	$3$	$6$

Since $0 \neq 36$ , there are no solutions.

No solution

Solve by Addition/Elimination 6x-2y=4 -9x+3y=12

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