Solve by Addition/Elimination 7x+2y=24 8x+2y=30

$7 x + 2 y = 24$ $8 x + 2 y = 30$

Step 1

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

$(- 1) \cdot (7 x + 2 y) = (- 1) (24)$

$8 x + 2 y = 30$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (7 x + 2 y)$ .

Apply the distributive property.

$- 1 (7 x) - 1 (2 y) = (- 1) (24)$

$8 x + 2 y = 30$

Multiply.

Multiply $7$ by $- 1$ .

$- 7 x - 1 (2 y) = (- 1) (24)$

$8 x + 2 y = 30$

Multiply $2$ by $- 1$ .

$- 7 x - 2 y = (- 1) (24)$

$8 x + 2 y = 30$

$- 7 x - 2 y = (- 1) (24)$

$8 x + 2 y = 30$

$- 7 x - 2 y = (- 1) (24)$

$8 x + 2 y = 30$

$- 7 x - 2 y = (- 1) (24)$

$8 x + 2 y = 30$

Simplify the right side.

Multiply $- 1$ by $24$ .

$- 7 x - 2 y = - 24$

$8 x + 2 y = 30$

$- 7 x - 2 y = - 24$

$8 x + 2 y = 30$

$- 7 x - 2 y = - 24$

$8 x + 2 y = 30$

Step 3

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

	$-$	$7$	$x$	$-$	$2$	$y$	$=$	$-$	$2$	$4$
$+$		$8$	$x$	$+$	$2$	$y$	$=$		$3$	$0$
			$x$				$=$			$6$

Step 4

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 $y$ .

$- 7 \cdot 6 - 2 y = - 24$

Multiply $- 7$ by $6$ .

$- 42 - 2 y = - 24$

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

Add $42$ to both sides of the equation.

$- 2 y = - 24 + 42$

Add $- 24$ and $42$ .

$- 2 y = 18$

Divide each term in $- 2 y = 18$ by $- 2$ and simplify.

Divide each term in $- 2 y = 18$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{18}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{18}{- 2}$

Divide $y$ by $1$ .

$y = \frac{18}{- 2}$

Simplify the right side.

Divide $18$ by $- 2$ .

$y = - 9$

Step 5

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

$(6, - 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(6, - 9)$

Equation Form:

$x = 6, y = - 9$

Step 7

Solve by Addition/Elimination 7x+2y=24 8x+2y=30

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