Solve by Addition/Elimination 5x+8y=-29 7x-2y=-67

$5 x + 8 y = - 29$ $7 x - 2 y = - 67$

Step 1

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

$5 x + 8 y = - 29$

$(4) \cdot (7 x - 2 y) = (4) (- 67)$

Step 2

Simplify.

Simplify the left side.

Simplify $(4) \cdot (7 x - 2 y)$ .

Apply the distributive property.

$5 x + 8 y = - 29$

$4 (7 x) + 4 (- 2 y) = (4) (- 67)$

Multiply.

Multiply $7$ by $4$ .

$5 x + 8 y = - 29$

$28 x + 4 (- 2 y) = (4) (- 67)$

Multiply $- 2$ by $4$ .

$5 x + 8 y = - 29$

$28 x - 8 y = (4) (- 67)$

$5 x + 8 y = - 29$

$28 x - 8 y = (4) (- 67)$

$5 x + 8 y = - 29$

$28 x - 8 y = (4) (- 67)$

$5 x + 8 y = - 29$

$28 x - 8 y = (4) (- 67)$

Simplify the right side.

Multiply $4$ by $- 67$ .

$5 x + 8 y = - 29$

$28 x - 8 y = - 268$

$5 x + 8 y = - 29$

$28 x - 8 y = - 268$

$5 x + 8 y = - 29$

$28 x - 8 y = - 268$

Step 3

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

		$5$	$x$	$+$	$8$	$y$	$=$		$-$	$2$	$9$
$+$	$2$	$8$	$x$	$-$	$8$	$y$	$=$	$-$	$2$	$6$	$8$
	$3$	$3$	$x$				$=$	$-$	$2$	$9$	$7$

Step 4

Divide each term in $33 x = - 297$ by $33$ and simplify.

Divide each term in $33 x = - 297$ by $33$ .

$\frac{33 x}{33} = \frac{- 297}{33}$

Simplify the left side.

Cancel the common factor of $33$ .

Cancel the common factor.

$\frac{33 x}{33} = \frac{- 297}{33}$

Divide $x$ by $1$ .

$x = \frac{- 297}{33}$

Simplify the right side.

Divide $- 297$ by $33$ .

$x = - 9$

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 $y$ .

$5 (- 9) + 8 y = - 29$

Multiply $5$ by $- 9$ .

$- 45 + 8 y = - 29$

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

Add $45$ to both sides of the equation.

$8 y = - 29 + 45$

Add $- 29$ and $45$ .

$8 y = 16$

Divide each term in $8 y = 16$ by $8$ and simplify.

Divide each term in $8 y = 16$ by $8$ .

$\frac{8 y}{8} = \frac{16}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{16}{8}$

Divide $y$ by $1$ .

$y = \frac{16}{8}$

Simplify the right side.

Divide $16$ by $8$ .

$y = 2$

Step 6

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

$(- 9, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 9, 2)$

Equation Form:

$x = - 9, y = 2$

Step 8

Solve by Addition/Elimination 5x+8y=-29 7x-2y=-67

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