Solve by Addition/Elimination 5x+7y=32 8x+6y=46

$5 x + 7 y = 32$ $8 x + 6 y = 46$

Step 1

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

$(- 8) \cdot (5 x + 7 y) = (- 8) (32)$

$(5) \cdot (8 x + 6 y) = (5) (46)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 8) \cdot (5 x + 7 y)$ .

Apply the distributive property.

$- 8 (5 x) - 8 (7 y) = (- 8) (32)$

$(5) \cdot (8 x + 6 y) = (5) (46)$

Multiply.

Multiply $5$ by $- 8$ .

$- 40 x - 8 (7 y) = (- 8) (32)$

$(5) \cdot (8 x + 6 y) = (5) (46)$

Multiply $7$ by $- 8$ .

$- 40 x - 56 y = (- 8) (32)$

$(5) \cdot (8 x + 6 y) = (5) (46)$

$- 40 x - 56 y = (- 8) (32)$

$(5) \cdot (8 x + 6 y) = (5) (46)$

$- 40 x - 56 y = (- 8) (32)$

$(5) \cdot (8 x + 6 y) = (5) (46)$

$- 40 x - 56 y = (- 8) (32)$

$(5) \cdot (8 x + 6 y) = (5) (46)$

Simplify the right side.

Multiply $- 8$ by $32$ .

$- 40 x - 56 y = - 256$

$(5) \cdot (8 x + 6 y) = (5) (46)$

$- 40 x - 56 y = - 256$

$(5) \cdot (8 x + 6 y) = (5) (46)$

Simplify the left side.

Simplify $(5) \cdot (8 x + 6 y)$ .

Apply the distributive property.

$- 40 x - 56 y = - 256$

$5 (8 x) + 5 (6 y) = (5) (46)$

Multiply.

Multiply $8$ by $5$ .

$- 40 x - 56 y = - 256$

$40 x + 5 (6 y) = (5) (46)$

Multiply $6$ by $5$ .

$- 40 x - 56 y = - 256$

$40 x + 30 y = (5) (46)$

$- 40 x - 56 y = - 256$

$40 x + 30 y = (5) (46)$

$- 40 x - 56 y = - 256$

$40 x + 30 y = (5) (46)$

$- 40 x - 56 y = - 256$

$40 x + 30 y = (5) (46)$

Simplify the right side.

Multiply $5$ by $46$ .

$- 40 x - 56 y = - 256$

$40 x + 30 y = 230$

$- 40 x - 56 y = - 256$

$40 x + 30 y = 230$

$- 40 x - 56 y = - 256$

$40 x + 30 y = 230$

Step 3

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

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

Step 4

Divide each term in $- 26 y = - 26$ by $- 26$ and simplify.

Divide each term in $- 26 y = - 26$ by $- 26$ .

$\frac{- 26 y}{- 26} = \frac{- 26}{- 26}$

Simplify the left side.

Cancel the common factor of $- 26$ .

Cancel the common factor.

$\frac{- 26 y}{- 26} = \frac{- 26}{- 26}$

Divide $y$ by $1$ .

$y = \frac{- 26}{- 26}$

Simplify the right side.

Divide $- 26$ by $- 26$ .

$y = 1$

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 $x$ .

$- 40 x - 56 \cdot 1 = - 256$

Multiply $- 56$ by $1$ .

$- 40 x - 56 = - 256$

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

Add $56$ to both sides of the equation.

$- 40 x = - 256 + 56$

Add $- 256$ and $56$ .

$- 40 x = - 200$

Divide each term in $- 40 x = - 200$ by $- 40$ and simplify.

Divide each term in $- 40 x = - 200$ by $- 40$ .

$\frac{- 40 x}{- 40} = \frac{- 200}{- 40}$

Simplify the left side.

Cancel the common factor of $- 40$ .

Cancel the common factor.

$\frac{- 40 x}{- 40} = \frac{- 200}{- 40}$

Divide $x$ by $1$ .

$x = \frac{- 200}{- 40}$

Simplify the right side.

Divide $- 200$ by $- 40$ .

$x = 5$

Step 6

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

$(5, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(5, 1)$

Equation Form:

$x = 5, y = 1$

Step 8

Solve by Addition/Elimination 5x+7y=32 8x+6y=46

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