Solve by Addition/Elimination 4x+6y=62 -6x+6y=-18

$4 x + 6 y = 62$ $- 6 x + 6 y = - 18$

Step 1

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

$(- 1) \cdot (4 x + 6 y) = (- 1) (62)$

$- 6 x + 6 y = - 18$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (4 x + 6 y)$ .

Apply the distributive property.

$- 1 (4 x) - 1 (6 y) = (- 1) (62)$

$- 6 x + 6 y = - 18$

Multiply.

Multiply $4$ by $- 1$ .

$- 4 x - 1 (6 y) = (- 1) (62)$

$- 6 x + 6 y = - 18$

Multiply $6$ by $- 1$ .

$- 4 x - 6 y = (- 1) (62)$

$- 6 x + 6 y = - 18$

$- 4 x - 6 y = (- 1) (62)$

$- 6 x + 6 y = - 18$

$- 4 x - 6 y = (- 1) (62)$

$- 6 x + 6 y = - 18$

$- 4 x - 6 y = (- 1) (62)$

$- 6 x + 6 y = - 18$

Simplify the right side.

Multiply $- 1$ by $62$ .

$- 4 x - 6 y = - 62$

$- 6 x + 6 y = - 18$

$- 4 x - 6 y = - 62$

$- 6 x + 6 y = - 18$

$- 4 x - 6 y = - 62$

$- 6 x + 6 y = - 18$

Step 3

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

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

Step 4

Divide each term in $- 10 x = - 80$ by $- 10$ and simplify.

Divide each term in $- 10 x = - 80$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{- 80}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{- 80}{- 10}$

Divide $x$ by $1$ .

$x = \frac{- 80}{- 10}$

Simplify the right side.

Divide $- 80$ by $- 10$ .

$x = 8$

Step 5

Substitute the value found for $x$ into one of the original equations, then solve for $y$ .

Substitute the value found for $x$ into one of the original equations to solve for $y$ .

$- 4 \cdot 8 - 6 y = - 62$

Multiply $- 4$ by $8$ .

$- 32 - 6 y = - 62$

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

Add $32$ to both sides of the equation.

$- 6 y = - 62 + 32$

Add $- 62$ and $32$ .

$- 6 y = - 30$

Divide each term in $- 6 y = - 30$ by $- 6$ and simplify.

Divide each term in $- 6 y = - 30$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 30}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 30}{- 6}$

Divide $y$ by $1$ .

$y = \frac{- 30}{- 6}$

Simplify the right side.

Divide $- 30$ by $- 6$ .

$y = 5$

Step 6

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

$(8, 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(8, 5)$

Equation Form:

$x = 8, y = 5$

Step 8

Solve by Addition/Elimination 4x+6y=62 -6x+6y=-18

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