Solve by Addition/Elimination 5x+6y=50 and x-6y=-26

$5 x + 6 y = 50$ and $x - 6 y = - 26$

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

$5 x + 6 y = 50$

$(- 5) \cdot (x - 6 y) = (- 5) (- 26)$

Simplify.

Simplify the left side.

Simplify $(- 5) \cdot (x - 6 y)$ .

Apply the distributive property.

$5 x + 6 y = 50$

$- 5 x - 5 (- 6 y) = (- 5) (- 26)$

Multiply $- 6$ by $- 5$ .

$5 x + 6 y = 50$

$- 5 x + 30 y = (- 5) (- 26)$

$5 x + 6 y = 50$

$- 5 x + 30 y = (- 5) (- 26)$

$5 x + 6 y = 50$

$- 5 x + 30 y = (- 5) (- 26)$

Simplify the right side.

Multiply $- 5$ by $- 26$ .

$5 x + 6 y = 50$

$- 5 x + 30 y = 130$

$5 x + 6 y = 50$

$- 5 x + 30 y = 130$

$5 x + 6 y = 50$

$- 5 x + 30 y = 130$

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

		$5$	$x$	$+$		$6$	$y$	$=$		$5$	$0$
$+$	$-$	$5$	$x$	$+$	$3$	$0$	$y$	$=$	$1$	$3$	$0$
					$3$	$6$	$y$	$=$	$1$	$8$	$0$

Divide each term in $36 y = 180$ by $36$ and simplify.

Divide each term in $36 y = 180$ by $36$ .

$\frac{36 y}{36} = \frac{180}{36}$

Simplify the left side.

Cancel the common factor of $36$ .

Cancel the common factor.

$\frac{36 y}{36} = \frac{180}{36}$

Divide $y$ by $1$ .

$y = \frac{180}{36}$

Simplify the right side.

Divide $180$ by $36$ .

$y = 5$

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 $x$ .

$5 x + 6 (5) = 50$

Multiply $6$ by $5$ .

$5 x + 30 = 50$

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

Subtract $30$ from both sides of the equation.

$5 x = 50 - 30$

Subtract $30$ from $50$ .

$5 x = 20$

Divide each term in $5 x = 20$ by $5$ and simplify.

Divide each term in $5 x = 20$ by $5$ .

$\frac{5 x}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{20}{5}$

Divide $x$ by $1$ .

$x = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$x = 4$

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

$(4, 5)$

The result can be shown in multiple forms.

Point Form:

$(4, 5)$

Equation Form:

$x = 4, y = 5$

Solve by Addition/Elimination 5x+6y=50 and x-6y=-26

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