Solve by Addition/Elimination 16x-10y=10 , -8x-6y=6

$16 x - 10 y = 10$ , $- 8 x - 6 y = 6$

Step 1

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

$16 x - 10 y = 10$

$(2) \cdot (- 8 x - 6 y) = (2) (6)$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (- 8 x - 6 y)$ .

Apply the distributive property.

$16 x - 10 y = 10$

$2 (- 8 x) + 2 (- 6 y) = (2) (6)$

Multiply.

Multiply $- 8$ by $2$ .

$16 x - 10 y = 10$

$- 16 x + 2 (- 6 y) = (2) (6)$

Multiply $- 6$ by $2$ .

$16 x - 10 y = 10$

$- 16 x - 12 y = (2) (6)$

$16 x - 10 y = 10$

$- 16 x - 12 y = (2) (6)$

$16 x - 10 y = 10$

$- 16 x - 12 y = (2) (6)$

$16 x - 10 y = 10$

$- 16 x - 12 y = (2) (6)$

Simplify the right side.

Multiply $2$ by $6$ .

$16 x - 10 y = 10$

$- 16 x - 12 y = 12$

$16 x - 10 y = 10$

$- 16 x - 12 y = 12$

$16 x - 10 y = 10$

$- 16 x - 12 y = 12$

Step 3

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

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

Step 4

Divide each term in $- 22 y = 22$ by $- 22$ and simplify.

Divide each term in $- 22 y = 22$ by $- 22$ .

$\frac{- 22 y}{- 22} = \frac{22}{- 22}$

Simplify the left side.

Cancel the common factor of $- 22$ .

Cancel the common factor.

$\frac{- 22 y}{- 22} = \frac{22}{- 22}$

Divide $y$ by $1$ .

$y = \frac{22}{- 22}$

Simplify the right side.

Divide $22$ by $- 22$ .

$y = - 1$

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 $x$ .

$16 x - 10 \cdot - 1 = 10$

Multiply $- 10$ by $- 1$ .

$16 x + 10 = 10$

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

Subtract $10$ from both sides of the equation.

$16 x = 10 - 10$

Subtract $10$ from $10$ .

$16 x = 0$

Divide each term in $16 x = 0$ by $16$ and simplify.

Divide each term in $16 x = 0$ by $16$ .

$\frac{16 x}{16} = \frac{0}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{0}{16}$

Divide $x$ by $1$ .

$x = \frac{0}{16}$

Simplify the right side.

Divide $0$ by $16$ .

$x = 0$

Step 6

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

$(0, - 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(0, - 1)$

Equation Form:

$x = 0, y = - 1$

Step 8

Solve by Addition/Elimination 16x-10y=10 , -8x-6y=6

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