Solve by Addition/Elimination 2x-6=4y 7y=-3x+9

$2 x - 6 = 4 y$ $7 y = - 3 x + 9$

Step 1

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

Subtract $4 y$ from both sides of the equation.

$2 x - 6 - 4 y = 0$

$7 y = - 3 x + 9$

Move $- 6$ .

$2 x - 4 y - 6 = 0$

$7 y = - 3 x + 9$

$2 x - 4 y - 6 = 0$

$7 y = - 3 x + 9$

Step 2

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

Add $3 x$ to both sides of the equation.

$7 y + 3 x = 9$

$2 x - 4 y - 6 = 0$

Reorder $7 y$ and $3 x$ .

$3 x + 7 y = 9$

$2 x - 4 y - 6 = 0$

$3 x + 7 y = 9$

$2 x - 4 y - 6 = 0$

Step 3

Add $6$ to both sides of the equation.

$2 x - 4 y = 6$

$3 x + 7 y = 9$

Step 4

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

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

$(2) \cdot (3 x + 7 y) = (2) (9)$

Step 5

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (2 x - 4 y)$ .

Apply the distributive property.

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

$(2) \cdot (3 x + 7 y) = (2) (9)$

Multiply.

Multiply $2$ by $- 3$ .

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

$(2) \cdot (3 x + 7 y) = (2) (9)$

Multiply $- 4$ by $- 3$ .

$- 6 x + 12 y = (- 3) (6)$

$(2) \cdot (3 x + 7 y) = (2) (9)$

$- 6 x + 12 y = (- 3) (6)$

$(2) \cdot (3 x + 7 y) = (2) (9)$

$- 6 x + 12 y = (- 3) (6)$

$(2) \cdot (3 x + 7 y) = (2) (9)$

$- 6 x + 12 y = (- 3) (6)$

$(2) \cdot (3 x + 7 y) = (2) (9)$

Simplify the right side.

Multiply $- 3$ by $6$ .

$- 6 x + 12 y = - 18$

$(2) \cdot (3 x + 7 y) = (2) (9)$

$- 6 x + 12 y = - 18$

$(2) \cdot (3 x + 7 y) = (2) (9)$

Simplify the left side.

Simplify $(2) \cdot (3 x + 7 y)$ .

Apply the distributive property.

$- 6 x + 12 y = - 18$

$2 (3 x) + 2 (7 y) = (2) (9)$

Multiply.

Multiply $3$ by $2$ .

$- 6 x + 12 y = - 18$

$6 x + 2 (7 y) = (2) (9)$

Multiply $7$ by $2$ .

$- 6 x + 12 y = - 18$

$6 x + 14 y = (2) (9)$

$- 6 x + 12 y = - 18$

$6 x + 14 y = (2) (9)$

$- 6 x + 12 y = - 18$

$6 x + 14 y = (2) (9)$

$- 6 x + 12 y = - 18$

$6 x + 14 y = (2) (9)$

Simplify the right side.

Multiply $2$ by $9$ .

$- 6 x + 12 y = - 18$

$6 x + 14 y = 18$

$- 6 x + 12 y = - 18$

$6 x + 14 y = 18$

$- 6 x + 12 y = - 18$

$6 x + 14 y = 18$

Step 6

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

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

Step 7

Divide each term in $26 y = 0$ by $26$ and simplify.

Divide each term in $26 y = 0$ by $26$ .

$\frac{26 y}{26} = \frac{0}{26}$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 y}{26} = \frac{0}{26}$

Divide $y$ by $1$ .

$y = \frac{0}{26}$

Simplify the right side.

Divide $0$ by $26$ .

$y = 0$

Step 8

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 $x$ .

$- 6 x + 12 (0) = - 18$

Simplify $- 6 x + 12 (0)$ .

Multiply $12$ by $0$ .

$- 6 x + 0 = - 18$

Add $- 6 x$ and $0$ .

$- 6 x = - 18$

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

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

$\frac{- 6 x}{- 6} = \frac{- 18}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 18}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 6}$

Simplify the right side.

Divide $- 18$ by $- 6$ .

$x = 3$

Step 9

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

$(3, 0)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(3, 0)$

Equation Form:

$x = 3, y = 0$

Step 11

Solve by Addition/Elimination 2x-6=4y 7y=-3x+9

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