Solve by Addition/Elimination -3x+8y=5 , 6x-2y=10

$- 3 x + 8 y = 5$ , $6 x - 2 y = 10$

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

$(2) \cdot (- 3 x + 8 y) = (2) (5)$

$6 x - 2 y = 10$

Simplify.

Simplify the left side.

Simplify $(2) \cdot (- 3 x + 8 y)$ .

Apply the distributive property.

$2 (- 3 x) + 2 (8 y) = (2) (5)$

$6 x - 2 y = 10$

Multiply.

Multiply $- 3$ by $2$ .

$- 6 x + 2 (8 y) = (2) (5)$

$6 x - 2 y = 10$

Multiply $8$ by $2$ .

$- 6 x + 16 y = (2) (5)$

$6 x - 2 y = 10$

$- 6 x + 16 y = (2) (5)$

$6 x - 2 y = 10$

$- 6 x + 16 y = (2) (5)$

$6 x - 2 y = 10$

$- 6 x + 16 y = (2) (5)$

$6 x - 2 y = 10$

Simplify the right side.

Multiply $2$ by $5$ .

$- 6 x + 16 y = 10$

$6 x - 2 y = 10$

$- 6 x + 16 y = 10$

$6 x - 2 y = 10$

$- 6 x + 16 y = 10$

$6 x - 2 y = 10$

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

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

Divide each term in $14 y = 20$ by $14$ and simplify.

Divide each term in $14 y = 20$ by $14$ .

$\frac{14 y}{14} = \frac{20}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 y}{14} = \frac{20}{14}$

Divide $y$ by $1$ .

$y = \frac{20}{14}$

Simplify the right side.

Cancel the common factor of $20$ and $14$ .

Factor $2$ out of $20$ .

$y = \frac{2 (10)}{14}$

Cancel the common factors.

Factor $2$ out of $14$ .

$y = \frac{2 \cdot 10}{2 \cdot 7}$

Cancel the common factor.

$y = \frac{2 \cdot 10}{2 \cdot 7}$

Rewrite the expression.

$y = \frac{10}{7}$

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 $x$ .

$- 6 x + 16 (\frac{10}{7}) = 10$

Multiply $16 (\frac{10}{7})$ .

Combine $16$ and $\frac{10}{7}$ .

$- 6 x + \frac{16 \cdot 10}{7} = 10$

Multiply $16$ by $10$ .

$- 6 x + \frac{160}{7} = 10$

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

Subtract $\frac{160}{7}$ from both sides of the equation.

$- 6 x = 10 - \frac{160}{7}$

To write $10$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- 6 x = 10 \cdot \frac{7}{7} - \frac{160}{7}$

Combine $10$ and $\frac{7}{7}$ .

$- 6 x = \frac{10 \cdot 7}{7} - \frac{160}{7}$

Combine the numerators over the common denominator.

$- 6 x = \frac{10 \cdot 7 - 160}{7}$

Simplify the numerator.

Multiply $10$ by $7$ .

$- 6 x = \frac{70 - 160}{7}$

Subtract $160$ from $70$ .

$- 6 x = \frac{- 90}{7}$

Move the negative in front of the fraction.

$- 6 x = - \frac{90}{7}$

Divide each term in $- 6 x = - \frac{90}{7}$ by $- 6$ and simplify.

Divide each term in $- 6 x = - \frac{90}{7}$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- \frac{90}{7}}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- \frac{90}{7}}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- \frac{90}{7}}{- 6}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{90}{7} \cdot \frac{1}{- 6}$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{90}{7}$ into the numerator.

$x = \frac{- 90}{7} \cdot \frac{1}{- 6}$

Factor $6$ out of $- 90$ .

$x = \frac{6 (- 15)}{7} \cdot \frac{1}{- 6}$

Factor $6$ out of $- 6$ .

$x = \frac{6 \cdot - 15}{7} \cdot \frac{1}{6 \cdot - 1}$

Cancel the common factor.

$x = \frac{6 \cdot - 15}{7} \cdot \frac{1}{6 \cdot - 1}$

Rewrite the expression.

$x = \frac{- 15}{7} \cdot \frac{1}{- 1}$

Multiply $\frac{- 15}{7}$ by $\frac{1}{- 1}$ .

$x = \frac{- 15}{7 \cdot - 1}$

Multiply $7$ by $- 1$ .

$x = \frac{- 15}{- 7}$

Dividing two negative values results in a positive value.

$x = \frac{15}{7}$

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

$(\frac{15}{7}, \frac{10}{7})$

The result can be shown in multiple forms.

Point Form:

$(\frac{15}{7}, \frac{10}{7})$

Equation Form:

$x = \frac{15}{7}, y = \frac{10}{7}$

Solve by Addition/Elimination -3x+8y=5 , 6x-2y=10

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