Solve by Addition/Elimination 5x=2y+50 2y+38=3x

$5 x = 2 y + 50$ $2 y + 38 = 3 x$

Step 1

Subtract $2 y$ from both sides of the equation.

$5 x - 2 y = 50$

$2 y + 38 = 3 x$

Step 2

Move all terms containing variables to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$2 y + 38 - 3 x = 0$

$5 x - 2 y = 50$

Move $38$ .

$2 y - 3 x + 38 = 0$

$5 x - 2 y = 50$

Reorder $2 y$ and $- 3 x$ .

$- 3 x + 2 y + 38 = 0$

$5 x - 2 y = 50$

$- 3 x + 2 y + 38 = 0$

$5 x - 2 y = 50$

Step 3

Subtract $38$ from both sides of the equation.

$- 3 x + 2 y = - 38$

$5 x - 2 y = 50$

Step 4

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

		$5$	$x$	$-$	$2$	$y$	$=$		$5$	$0$
$+$	$-$	$3$	$x$	$+$	$2$	$y$	$=$	$-$	$3$	$8$
		$2$	$x$				$=$		$1$	$2$

Step 5

Divide each term in $2 x = 12$ by $2$ and simplify.

Divide each term in $2 x = 12$ by $2$ .

$\frac{2 x}{2} = \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{12}{2}$

Divide $x$ by $1$ .

$x = \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$x = 6$

Step 6

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 $y$ .

$5 (6) - 2 y = 50$

Multiply $5$ by $6$ .

$30 - 2 y = 50$

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

Subtract $30$ from both sides of the equation.

$- 2 y = 50 - 30$

Subtract $30$ from $50$ .

$- 2 y = 20$

Divide each term in $- 2 y = 20$ by $- 2$ and simplify.

Divide each term in $- 2 y = 20$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{20}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{20}{- 2}$

Divide $y$ by $1$ .

$y = \frac{20}{- 2}$

Simplify the right side.

Divide $20$ by $- 2$ .

$y = - 10$

Step 7

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

$(6, - 10)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(6, - 10)$

Equation Form:

$x = 6, y = - 10$

Step 9

Solve by Addition/Elimination 5x=2y+50 2y+38=3x

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