Solve by Addition/Elimination 0=-2y+10-6x 14-22y=18x

$0 = - 2 y + 10 - 6 x$ $14 - 22 y = 18 x$

Step 1

Simplify the right side.

Simplify $- 2 y + 10 - 6 x$ .

Move $10$ .

$0 = - 2 y - 6 x + 10$

$14 - 22 y = 18 x$

Reorder $- 2 y$ and $- 6 x$ .

$0 = - 6 x - 2 y + 10$

$14 - 22 y = 18 x$

$0 = - 6 x - 2 y + 10$

$14 - 22 y = 18 x$

$0 = - 6 x - 2 y + 10$

$14 - 22 y = 18 x$

Step 2

Simplify the left side.

Reorder $14$ and $- 22 y$ .

$- 22 y + 14 = 18 x$

$0 = - 6 x - 2 y + 10$

$- 22 y + 14 = 18 x$

$0 = - 6 x - 2 y + 10$

Step 3

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

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

$6 x = - 2 y + 10$

$- 22 y + 14 = 18 x$

Add $2 y$ to both sides of the equation.

$6 x + 2 y = 10$

$- 22 y + 14 = 18 x$

$6 x + 2 y = 10$

$- 22 y + 14 = 18 x$

Step 4

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

Subtract $18 x$ from both sides of the equation.

$- 22 y + 14 - 18 x = 0$

$6 x + 2 y = 10$

Move $14$ .

$- 22 y - 18 x + 14 = 0$

$6 x + 2 y = 10$

Reorder $- 22 y$ and $- 18 x$ .

$- 18 x - 22 y + 14 = 0$

$6 x + 2 y = 10$

$- 18 x - 22 y + 14 = 0$

$6 x + 2 y = 10$

Step 5

Subtract $14$ from both sides of the equation.

$- 18 x - 22 y = - 14$

$6 x + 2 y = 10$

Step 6

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

$(3) \cdot (6 x + 2 y) = (3) (10)$

$- 18 x - 22 y = - 14$

Step 7

Simplify.

Simplify the left side.

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

Apply the distributive property.

$3 (6 x) + 3 (2 y) = (3) (10)$

$- 18 x - 22 y = - 14$

Multiply.

Multiply $6$ by $3$ .

$18 x + 3 (2 y) = (3) (10)$

$- 18 x - 22 y = - 14$

Multiply $2$ by $3$ .

$18 x + 6 y = (3) (10)$

$- 18 x - 22 y = - 14$

$18 x + 6 y = (3) (10)$

$- 18 x - 22 y = - 14$

$18 x + 6 y = (3) (10)$

$- 18 x - 22 y = - 14$

$18 x + 6 y = (3) (10)$

$- 18 x - 22 y = - 14$

Simplify the right side.

Multiply $3$ by $10$ .

$18 x + 6 y = 30$

$- 18 x - 22 y = - 14$

$18 x + 6 y = 30$

$- 18 x - 22 y = - 14$

$18 x + 6 y = 30$

$- 18 x - 22 y = - 14$

Step 8

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

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

Step 9

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

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

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

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $16$ by $- 16$ .

$y = - 1$

Step 10

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 $x$ .

$18 x + 6 (- 1) = 30$

Multiply $6$ by $- 1$ .

$18 x - 6 = 30$

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

Add $6$ to both sides of the equation.

$18 x = 30 + 6$

Add $30$ and $6$ .

$18 x = 36$

Divide each term in $18 x = 36$ by $18$ and simplify.

Divide each term in $18 x = 36$ by $18$ .

$\frac{18 x}{18} = \frac{36}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 x}{18} = \frac{36}{18}$

Divide $x$ by $1$ .

$x = \frac{36}{18}$

Simplify the right side.

Divide $36$ by $18$ .

$x = 2$

Step 11

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

$(2, - 1)$

Step 12

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 13

Solve by Addition/Elimination 0=-2y+10-6x 14-22y=18x

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