Algebra Examples

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

Step 1

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

$- 3 y = - 5 - 2 x$

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

Step 2

Divide each term in $- 3 y = - 5 - 2 x$ by $- 3$ and simplify.

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Step 2.1

Divide each term in $- 3 y = - 5 - 2 x$ by $- 3$ .

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.1.1

Cancel the common factor.

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

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

Step 2.2.1.2

Divide $y$ by $1$ .

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

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

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

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

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

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Dividing two negative values results in a positive value.

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

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

Step 2.3.1.2

Dividing two negative values results in a positive value.

$y = \frac{5}{3} + \frac{2 x}{3}$

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

$y = \frac{5}{3} + \frac{2 x}{3}$

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

$y = \frac{5}{3} + \frac{2 x}{3}$

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

$y = \frac{5}{3} + \frac{2 x}{3}$

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

Step 3

Subtract $x$ from both sides of the equation.

$\frac{y}{11} = 50 - x$

$y = \frac{5}{3} + \frac{2 x}{3}$

Step 4

Multiply both sides of the equation by $11$ .

$11 (\frac{y}{11}) = 11 (50 - x)$

$y = \frac{5}{3} + \frac{2 x}{3}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $11$ .

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Step 5.1.1.1

Cancel the common factor.

$11 (\frac{y}{11}) = 11 (50 - x)$

$y = \frac{5}{3} + \frac{2 x}{3}$

Step 5.1.1.2

Rewrite the expression.

$y = 11 (50 - x)$

$y = \frac{5}{3} + \frac{2 x}{3}$

$y = 11 (50 - x)$

$y = \frac{5}{3} + \frac{2 x}{3}$

$y = 11 (50 - x)$

$y = \frac{5}{3} + \frac{2 x}{3}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $11 (50 - x)$ .

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Step 5.2.1.1

Apply the distributive property.

$y = 11 \cdot 50 + 11 (- x)$

$y = \frac{5}{3} + \frac{2 x}{3}$

Step 5.2.1.2

Multiply.

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Step 5.2.1.2.1

Multiply $11$ by $50$ .

$y = 550 + 11 (- x)$

$y = \frac{5}{3} + \frac{2 x}{3}$

Step 5.2.1.2.2

Multiply $- 1$ by $11$ .

$y = 550 - 11 x$

$y = \frac{5}{3} + \frac{2 x}{3}$

$y = 550 - 11 x$

$y = \frac{5}{3} + \frac{2 x}{3}$

$y = 550 - 11 x$

$y = \frac{5}{3} + \frac{2 x}{3}$

$y = 550 - 11 x$

$y = \frac{5}{3} + \frac{2 x}{3}$

$y = 550 - 11 x$

$y = \frac{5}{3} + \frac{2 x}{3}$

Step 6

Reorder $550$ and $- 11 x$ .

$y = - 11 x + 550$

$y = \frac{5}{3} + \frac{2 x}{3}$

Step 7

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(47, 33)$

Step 8