Solve by Addition/Elimination -7x-8y=9 , -4x+9y=-22

$- 7 x - 8 y = 9$ , $- 4 x + 9 y = - 22$

Step 1

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

$(- 4) \cdot (- 7 x - 8 y) = (- 4) (9)$

$(7) \cdot (- 4 x + 9 y) = (7) (- 22)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 4) \cdot (- 7 x - 8 y)$ .

Apply the distributive property.

$- 4 (- 7 x) - 4 (- 8 y) = (- 4) (9)$

$(7) \cdot (- 4 x + 9 y) = (7) (- 22)$

Multiply.

Multiply $- 7$ by $- 4$ .

$28 x - 4 (- 8 y) = (- 4) (9)$

$(7) \cdot (- 4 x + 9 y) = (7) (- 22)$

Multiply $- 8$ by $- 4$ .

$28 x + 32 y = (- 4) (9)$

$(7) \cdot (- 4 x + 9 y) = (7) (- 22)$

$28 x + 32 y = (- 4) (9)$

$(7) \cdot (- 4 x + 9 y) = (7) (- 22)$

$28 x + 32 y = (- 4) (9)$

$(7) \cdot (- 4 x + 9 y) = (7) (- 22)$

$28 x + 32 y = (- 4) (9)$

$(7) \cdot (- 4 x + 9 y) = (7) (- 22)$

Simplify the right side.

Multiply $- 4$ by $9$ .

$28 x + 32 y = - 36$

$(7) \cdot (- 4 x + 9 y) = (7) (- 22)$

$28 x + 32 y = - 36$

$(7) \cdot (- 4 x + 9 y) = (7) (- 22)$

Simplify the left side.

Simplify $(7) \cdot (- 4 x + 9 y)$ .

Apply the distributive property.

$28 x + 32 y = - 36$

$7 (- 4 x) + 7 (9 y) = (7) (- 22)$

Multiply.

Multiply $- 4$ by $7$ .

$28 x + 32 y = - 36$

$- 28 x + 7 (9 y) = (7) (- 22)$

Multiply $9$ by $7$ .

$28 x + 32 y = - 36$

$- 28 x + 63 y = (7) (- 22)$

$28 x + 32 y = - 36$

$- 28 x + 63 y = (7) (- 22)$

$28 x + 32 y = - 36$

$- 28 x + 63 y = (7) (- 22)$

$28 x + 32 y = - 36$

$- 28 x + 63 y = (7) (- 22)$

Simplify the right side.

Multiply $7$ by $- 22$ .

$28 x + 32 y = - 36$

$- 28 x + 63 y = - 154$

$28 x + 32 y = - 36$

$- 28 x + 63 y = - 154$

$28 x + 32 y = - 36$

$- 28 x + 63 y = - 154$

Step 3

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

		$2$	$8$	$x$	$+$	$3$	$2$	$y$	$=$		$-$	$3$	$6$
$+$	$-$	$2$	$8$	$x$	$+$	$6$	$3$	$y$	$=$	$-$	$1$	$5$	$4$
						$9$	$5$	$y$	$=$	$-$	$1$	$9$	$0$

Step 4

Divide each term in $95 y = - 190$ by $95$ and simplify.

Divide each term in $95 y = - 190$ by $95$ .

$\frac{95 y}{95} = \frac{- 190}{95}$

Simplify the left side.

Cancel the common factor of $95$ .

Cancel the common factor.

$\frac{95 y}{95} = \frac{- 190}{95}$

Divide $y$ by $1$ .

$y = \frac{- 190}{95}$

Simplify the right side.

Divide $- 190$ by $95$ .

$y = - 2$

Step 5

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 $x$ .

$28 x + 32 (- 2) = - 36$

Multiply $32$ by $- 2$ .

$28 x - 64 = - 36$

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

Add $64$ to both sides of the equation.

$28 x = - 36 + 64$

Add $- 36$ and $64$ .

$28 x = 28$

Divide each term in $28 x = 28$ by $28$ and simplify.

Divide each term in $28 x = 28$ by $28$ .

$\frac{28 x}{28} = \frac{28}{28}$

Simplify the left side.

Cancel the common factor of $28$ .

Cancel the common factor.

$\frac{28 x}{28} = \frac{28}{28}$

Divide $x$ by $1$ .

$x = \frac{28}{28}$

Simplify the right side.

Divide $28$ by $28$ .

$x = 1$

Step 6

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

$(1, - 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(1, - 2)$

Equation Form:

$x = 1, y = - 2$

Step 8

Solve by Addition/Elimination -7x-8y=9 , -4x+9y=-22

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