Solve by Addition/Elimination 2x+7y=-38 -5x-8y=38

$2 x + 7 y = - 38$ $- 5 x - 8 y = 38$

Step 1

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

$(5) \cdot (2 x + 7 y) = (5) (- 38)$

$(2) \cdot (- 5 x - 8 y) = (2) (38)$

Step 2

Simplify.

Simplify the left side.

Simplify $(5) \cdot (2 x + 7 y)$ .

Apply the distributive property.

$5 (2 x) + 5 (7 y) = (5) (- 38)$

$(2) \cdot (- 5 x - 8 y) = (2) (38)$

Multiply.

Multiply $2$ by $5$ .

$10 x + 5 (7 y) = (5) (- 38)$

$(2) \cdot (- 5 x - 8 y) = (2) (38)$

Multiply $7$ by $5$ .

$10 x + 35 y = (5) (- 38)$

$(2) \cdot (- 5 x - 8 y) = (2) (38)$

$10 x + 35 y = (5) (- 38)$

$(2) \cdot (- 5 x - 8 y) = (2) (38)$

$10 x + 35 y = (5) (- 38)$

$(2) \cdot (- 5 x - 8 y) = (2) (38)$

$10 x + 35 y = (5) (- 38)$

$(2) \cdot (- 5 x - 8 y) = (2) (38)$

Simplify the right side.

Multiply $5$ by $- 38$ .

$10 x + 35 y = - 190$

$(2) \cdot (- 5 x - 8 y) = (2) (38)$

$10 x + 35 y = - 190$

$(2) \cdot (- 5 x - 8 y) = (2) (38)$

Simplify the left side.

Simplify $(2) \cdot (- 5 x - 8 y)$ .

Apply the distributive property.

$10 x + 35 y = - 190$

$2 (- 5 x) + 2 (- 8 y) = (2) (38)$

Multiply.

Multiply $- 5$ by $2$ .

$10 x + 35 y = - 190$

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

Multiply $- 8$ by $2$ .

$10 x + 35 y = - 190$

$- 10 x - 16 y = (2) (38)$

$10 x + 35 y = - 190$

$- 10 x - 16 y = (2) (38)$

$10 x + 35 y = - 190$

$- 10 x - 16 y = (2) (38)$

$10 x + 35 y = - 190$

$- 10 x - 16 y = (2) (38)$

Simplify the right side.

Multiply $2$ by $38$ .

$10 x + 35 y = - 190$

$- 10 x - 16 y = 76$

$10 x + 35 y = - 190$

$- 10 x - 16 y = 76$

$10 x + 35 y = - 190$

$- 10 x - 16 y = 76$

Step 3

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

		$1$	$0$	$x$	$+$	$3$	$5$	$y$	$=$	$-$	$1$	$9$	$0$
$+$	$-$	$1$	$0$	$x$	$-$	$1$	$6$	$y$	$=$			$7$	$6$
						$1$	$9$	$y$	$=$	$-$	$1$	$1$	$4$

Step 4

Divide each term in $19 y = - 114$ by $19$ and simplify.

Divide each term in $19 y = - 114$ by $19$ .

$\frac{19 y}{19} = \frac{- 114}{19}$

Simplify the left side.

Cancel the common factor of $19$ .

Cancel the common factor.

$\frac{19 y}{19} = \frac{- 114}{19}$

Divide $y$ by $1$ .

$y = \frac{- 114}{19}$

Simplify the right side.

Divide $- 114$ by $19$ .

$y = - 6$

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 $x$ .

$10 x + 35 (- 6) = - 190$

Multiply $35$ by $- 6$ .

$10 x - 210 = - 190$

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

Add $210$ to both sides of the equation.

$10 x = - 190 + 210$

Add $- 190$ and $210$ .

$10 x = 20$

Divide each term in $10 x = 20$ by $10$ and simplify.

Divide each term in $10 x = 20$ by $10$ .

$\frac{10 x}{10} = \frac{20}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{20}{10}$

Divide $x$ by $1$ .

$x = \frac{20}{10}$

Simplify the right side.

Divide $20$ by $10$ .

$x = 2$

Step 6

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

$(2, - 6)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, - 6)$

Equation Form:

$x = 2, y = - 6$

Step 8

Solve by Addition/Elimination 2x+7y=-38 -5x-8y=38

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