Solve by Linear Combination 2x-3y=-5 , x+y/11=50

$2 x - 3 y = - 5$ , $x + \frac{y}{11} = 50$

Step 1

Multiply each term in $x + \frac{y}{11} = 50$ by $11$ to eliminate the fractions.

Multiply each term in $x + \frac{y}{11} = 50$ by $11$ .

$x \cdot 11 + \frac{y}{11} \cdot 11 = 50 \cdot 11$

$2 x - 3 y = - 5$

Simplify the left side.

Simplify each term.

Move $11$ to the left of $x$ .

$11 \cdot x + \frac{y}{11} \cdot 11 = 50 \cdot 11$

$2 x - 3 y = - 5$

Cancel the common factor of $11$ .

Cancel the common factor.

$11 x + \frac{y}{11} \cdot 11 = 50 \cdot 11$

$2 x - 3 y = - 5$

Rewrite the expression.

$11 x + y = 50 \cdot 11$

$2 x - 3 y = - 5$

$11 x + y = 50 \cdot 11$

$2 x - 3 y = - 5$

$11 x + y = 50 \cdot 11$

$2 x - 3 y = - 5$

$11 x + y = 50 \cdot 11$

$2 x - 3 y = - 5$

Simplify the right side.

Multiply $50$ by $11$ .

$11 x + y = 550$

$2 x - 3 y = - 5$

$11 x + y = 550$

$2 x - 3 y = - 5$

$11 x + y = 550$

$2 x - 3 y = - 5$

Step 2

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

$2 x - 3 y = - 5$

$(3) \cdot (11 x + y) = (3) (550)$

Step 3

Simplify.

Simplify the left side.

Simplify $(3) \cdot (11 x + y)$ .

Apply the distributive property.

$2 x - 3 y = - 5$

$3 (11 x) + 3 y = (3) (550)$

Multiply $11$ by $3$ .

$2 x - 3 y = - 5$

$33 x + 3 y = (3) (550)$

$2 x - 3 y = - 5$

$33 x + 3 y = (3) (550)$

$2 x - 3 y = - 5$

$33 x + 3 y = (3) (550)$

Simplify the right side.

Multiply $3$ by $550$ .

$2 x - 3 y = - 5$

$33 x + 3 y = 1650$

$2 x - 3 y = - 5$

$33 x + 3 y = 1650$

$2 x - 3 y = - 5$

$33 x + 3 y = 1650$

Step 4

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

		$2$	$x$	$-$	$3$	$y$	$=$			$-$	$5$
$+$	$3$	$3$	$x$	$+$	$3$	$y$	$=$	$1$	$6$	$5$	$0$
	$3$	$5$	$x$				$=$	$1$	$6$	$4$	$5$

Step 5

Divide each term in $35 x = 1645$ by $35$ and simplify.

Divide each term in $35 x = 1645$ by $35$ .

$\frac{35 x}{35} = \frac{1645}{35}$

Simplify the left side.

Cancel the common factor of $35$ .

Cancel the common factor.

$\frac{35 x}{35} = \frac{1645}{35}$

Divide $x$ by $1$ .

$x = \frac{1645}{35}$

Simplify the right side.

Divide $1645$ by $35$ .

$x = 47$

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 $y$ .

$2 (47) - 3 y = - 5$

Multiply $2$ by $47$ .

$94 - 3 y = - 5$

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

Subtract $94$ from both sides of the equation.

$- 3 y = - 5 - 94$

Subtract $94$ from $- 5$ .

$- 3 y = - 99$

Divide each term in $- 3 y = - 99$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 99$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 99}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 99}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 99}{- 3}$

Simplify the right side.

Divide $- 99$ by $- 3$ .

$y = 33$

Step 7

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

$(47, 33)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(47, 33)$

Equation Form:

$x = 47, y = 33$

Step 9

Solve by Linear Combination 2x-3y=-5 , x+y/11=50

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