Solve by Addition/Elimination 8x+14y=4 -6x-7y=-10

$8 x + 14 y = 4$ $- 6 x - 7 y = - 10$

Step 1

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

$8 x + 14 y = 4$

$(2) \cdot (- 6 x - 7 y) = (2) (- 10)$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (- 6 x - 7 y)$ .

Apply the distributive property.

$8 x + 14 y = 4$

$2 (- 6 x) + 2 (- 7 y) = (2) (- 10)$

Multiply.

Multiply $- 6$ by $2$ .

$8 x + 14 y = 4$

$- 12 x + 2 (- 7 y) = (2) (- 10)$

Multiply $- 7$ by $2$ .

$8 x + 14 y = 4$

$- 12 x - 14 y = (2) (- 10)$

$8 x + 14 y = 4$

$- 12 x - 14 y = (2) (- 10)$

$8 x + 14 y = 4$

$- 12 x - 14 y = (2) (- 10)$

$8 x + 14 y = 4$

$- 12 x - 14 y = (2) (- 10)$

Simplify the right side.

Multiply $2$ by $- 10$ .

$8 x + 14 y = 4$

$- 12 x - 14 y = - 20$

$8 x + 14 y = 4$

$- 12 x - 14 y = - 20$

$8 x + 14 y = 4$

$- 12 x - 14 y = - 20$

Step 3

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

			$8$	$x$	$+$	$1$	$4$	$y$	$=$			$4$
$+$	$-$	$1$	$2$	$x$	$-$	$1$	$4$	$y$	$=$	$-$	$2$	$0$
		$-$	$4$	$x$					$=$	$-$	$1$	$6$

Step 4

Divide each term in $- 4 x = - 16$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 16$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 16}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 16}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 16}{- 4}$

Simplify the right side.

Divide $- 16$ by $- 4$ .

$x = 4$

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 $y$ .

$8 (4) + 14 y = 4$

Multiply $8$ by $4$ .

$32 + 14 y = 4$

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

Subtract $32$ from both sides of the equation.

$14 y = 4 - 32$

Subtract $32$ from $4$ .

$14 y = - 28$

Divide each term in $14 y = - 28$ by $14$ and simplify.

Divide each term in $14 y = - 28$ by $14$ .

$\frac{14 y}{14} = \frac{- 28}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 y}{14} = \frac{- 28}{14}$

Divide $y$ by $1$ .

$y = \frac{- 28}{14}$

Simplify the right side.

Divide $- 28$ by $14$ .

$y = - 2$

Step 6

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

$(4, - 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, - 2)$

Equation Form:

$x = 4, y = - 2$

Step 8

Solve by Addition/Elimination 8x+14y=4 -6x-7y=-10

Related Questions

Support LCMGCF.com by disabling your adblocker.