Solve by Addition/Elimination 3x+5y=44 8x-7y=-25

$3 x + 5 y = 44$ $8 x - 7 y = - 25$

Step 1

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

$(- 8) \cdot (3 x + 5 y) = (- 8) (44)$

$(3) \cdot (8 x - 7 y) = (3) (- 25)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 8) \cdot (3 x + 5 y)$ .

Apply the distributive property.

$- 8 (3 x) - 8 (5 y) = (- 8) (44)$

$(3) \cdot (8 x - 7 y) = (3) (- 25)$

Multiply.

Multiply $3$ by $- 8$ .

$- 24 x - 8 (5 y) = (- 8) (44)$

$(3) \cdot (8 x - 7 y) = (3) (- 25)$

Multiply $5$ by $- 8$ .

$- 24 x - 40 y = (- 8) (44)$

$(3) \cdot (8 x - 7 y) = (3) (- 25)$

$- 24 x - 40 y = (- 8) (44)$

$(3) \cdot (8 x - 7 y) = (3) (- 25)$

$- 24 x - 40 y = (- 8) (44)$

$(3) \cdot (8 x - 7 y) = (3) (- 25)$

$- 24 x - 40 y = (- 8) (44)$

$(3) \cdot (8 x - 7 y) = (3) (- 25)$

Simplify the right side.

Multiply $- 8$ by $44$ .

$- 24 x - 40 y = - 352$

$(3) \cdot (8 x - 7 y) = (3) (- 25)$

$- 24 x - 40 y = - 352$

$(3) \cdot (8 x - 7 y) = (3) (- 25)$

Simplify the left side.

Simplify $(3) \cdot (8 x - 7 y)$ .

Apply the distributive property.

$- 24 x - 40 y = - 352$

$3 (8 x) + 3 (- 7 y) = (3) (- 25)$

Multiply.

Multiply $8$ by $3$ .

$- 24 x - 40 y = - 352$

$24 x + 3 (- 7 y) = (3) (- 25)$

Multiply $- 7$ by $3$ .

$- 24 x - 40 y = - 352$

$24 x - 21 y = (3) (- 25)$

$- 24 x - 40 y = - 352$

$24 x - 21 y = (3) (- 25)$

$- 24 x - 40 y = - 352$

$24 x - 21 y = (3) (- 25)$

$- 24 x - 40 y = - 352$

$24 x - 21 y = (3) (- 25)$

Simplify the right side.

Multiply $3$ by $- 25$ .

$- 24 x - 40 y = - 352$

$24 x - 21 y = - 75$

$- 24 x - 40 y = - 352$

$24 x - 21 y = - 75$

$- 24 x - 40 y = - 352$

$24 x - 21 y = - 75$

Step 3

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

	$-$	$2$	$4$	$x$	$-$	$4$	$0$	$y$	$=$	$-$	$3$	$5$	$2$
$+$		$2$	$4$	$x$	$-$	$2$	$1$	$y$	$=$		$-$	$7$	$5$
					$-$	$6$	$1$	$y$	$=$	$-$	$4$	$2$	$7$

Step 4

Divide each term in $- 61 y = - 427$ by $- 61$ and simplify.

Divide each term in $- 61 y = - 427$ by $- 61$ .

$\frac{- 61 y}{- 61} = \frac{- 427}{- 61}$

Simplify the left side.

Cancel the common factor of $- 61$ .

Cancel the common factor.

$\frac{- 61 y}{- 61} = \frac{- 427}{- 61}$

Divide $y$ by $1$ .

$y = \frac{- 427}{- 61}$

Simplify the right side.

Divide $- 427$ by $- 61$ .

$y = 7$

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 $x$ .

$- 24 x - 40 \cdot 7 = - 352$

Multiply $- 40$ by $7$ .

$- 24 x - 280 = - 352$

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

Add $280$ to both sides of the equation.

$- 24 x = - 352 + 280$

Add $- 352$ and $280$ .

$- 24 x = - 72$

Divide each term in $- 24 x = - 72$ by $- 24$ and simplify.

Divide each term in $- 24 x = - 72$ by $- 24$ .

$\frac{- 24 x}{- 24} = \frac{- 72}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 x}{- 24} = \frac{- 72}{- 24}$

Divide $x$ by $1$ .

$x = \frac{- 72}{- 24}$

Simplify the right side.

Divide $- 72$ by $- 24$ .

$x = 3$

Step 6

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

$(3, 7)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(3, 7)$

Equation Form:

$x = 3, y = 7$

Step 8

Solve by Addition/Elimination 3x+5y=44 8x-7y=-25

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