Solve by Addition/Elimination 3x+8y=2 5x-4y=38

$3 x + 8 y = 2$ $5 x - 4 y = 38$

Step 1

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

$3 x + 8 y = 2$

$(2) \cdot (5 x - 4 y) = (2) (38)$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (5 x - 4 y)$ .

Apply the distributive property.

$3 x + 8 y = 2$

$2 (5 x) + 2 (- 4 y) = (2) (38)$

Multiply.

Multiply $5$ by $2$ .

$3 x + 8 y = 2$

$10 x + 2 (- 4 y) = (2) (38)$

Multiply $- 4$ by $2$ .

$3 x + 8 y = 2$

$10 x - 8 y = (2) (38)$

$3 x + 8 y = 2$

$10 x - 8 y = (2) (38)$

$3 x + 8 y = 2$

$10 x - 8 y = (2) (38)$

$3 x + 8 y = 2$

$10 x - 8 y = (2) (38)$

Simplify the right side.

Multiply $2$ by $38$ .

$3 x + 8 y = 2$

$10 x - 8 y = 76$

$3 x + 8 y = 2$

$10 x - 8 y = 76$

$3 x + 8 y = 2$

$10 x - 8 y = 76$

Step 3

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

		$3$	$x$	$+$	$8$	$y$	$=$		$2$
$+$	$1$	$0$	$x$	$-$	$8$	$y$	$=$	$7$	$6$
	$1$	$3$	$x$				$=$	$7$	$8$

Step 4

Divide each term in $13 x = 78$ by $13$ and simplify.

Divide each term in $13 x = 78$ by $13$ .

$\frac{13 x}{13} = \frac{78}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} = \frac{78}{13}$

Divide $x$ by $1$ .

$x = \frac{78}{13}$

Simplify the right side.

Divide $78$ by $13$ .

$x = 6$

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 $y$ .

$3 (6) + 8 y = 2$

Multiply $3$ by $6$ .

$18 + 8 y = 2$

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

Subtract $18$ from both sides of the equation.

$8 y = 2 - 18$

Subtract $18$ from $2$ .

$8 y = - 16$

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.

$(6, - 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(6, - 2)$

Equation Form:

$x = 6, y = - 2$

Step 8

Solve by Addition/Elimination 3x+8y=2 5x-4y=38

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