Algebra Examples

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

Step 1

Subtract $\frac{y}{11}$ from both sides of the equation.

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

$2 x - 3 y = - 5$

Step 2

Replace all occurrences of $x$ with $50 - \frac{y}{11}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $2 x - 3 y = - 5$ with $50 - \frac{y}{11}$ .

$2 (50 - \frac{y}{11}) - 3 y = - 5$

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (50 - \frac{y}{11}) - 3 y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$2 \cdot 50 + 2 (- \frac{y}{11}) - 3 y = - 5$

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

Step 2.2.1.1.2

Multiply $2$ by $50$ .

$100 + 2 (- \frac{y}{11}) - 3 y = - 5$

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

Step 2.2.1.1.3

Multiply $2 (- \frac{y}{11})$ .

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Step 2.2.1.1.3.1

Multiply $- 1$ by $2$ .

$100 - 2 \frac{y}{11} - 3 y = - 5$

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

Step 2.2.1.1.3.2

Combine $- 2$ and $\frac{y}{11}$ .

$100 + \frac{- 2 y}{11} - 3 y = - 5$

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

$100 + \frac{- 2 y}{11} - 3 y = - 5$

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

Step 2.2.1.1.4

Move the negative in front of the fraction.

$100 - \frac{2 y}{11} - 3 y = - 5$

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

$100 - \frac{2 y}{11} - 3 y = - 5$

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

Step 2.2.1.2

To write $- 3 y$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$100 - \frac{2 y}{11} - 3 y \cdot \frac{11}{11} = - 5$

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

Step 2.2.1.3

Simplify terms.

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Step 2.2.1.3.1

Combine $- 3 y$ and $\frac{11}{11}$ .

$100 - \frac{2 y}{11} + \frac{- 3 y \cdot 11}{11} = - 5$

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

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$100 + \frac{- 2 y - 3 y \cdot 11}{11} = - 5$

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

$100 + \frac{- 2 y - 3 y \cdot 11}{11} = - 5$

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

Step 2.2.1.4

Simplify each term.

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Step 2.2.1.4.1

Simplify the numerator.

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Step 2.2.1.4.1.1

Factor $y$ out of $- 2 y - 3 y \cdot 11$ .

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Step 2.2.1.4.1.1.1

Factor $y$ out of $- 2 y$ .

$100 + \frac{y \cdot - 2 - 3 y \cdot 11}{11} = - 5$

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

Step 2.2.1.4.1.1.2

Factor $y$ out of $- 3 y \cdot 11$ .

$100 + \frac{y \cdot - 2 + y (- 3 \cdot 11)}{11} = - 5$

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

Step 2.2.1.4.1.1.3

Factor $y$ out of $y \cdot - 2 + y (- 3 \cdot 11)$ .

$100 + \frac{y (- 2 - 3 \cdot 11)}{11} = - 5$

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

$100 + \frac{y (- 2 - 3 \cdot 11)}{11} = - 5$

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

Step 2.2.1.4.1.2

Multiply $- 3$ by $11$ .

$100 + \frac{y (- 2 - 33)}{11} = - 5$

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

Step 2.2.1.4.1.3

Subtract $33$ from $- 2$ .

$100 + \frac{y \cdot - 35}{11} = - 5$

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

$100 + \frac{y \cdot - 35}{11} = - 5$

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

Step 2.2.1.4.2

Move $- 35$ to the left of $y$ .

$100 + \frac{- 35 \cdot y}{11} = - 5$

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

Step 2.2.1.4.3

Move the negative in front of the fraction.

$100 - \frac{35 y}{11} = - 5$

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

$100 - \frac{35 y}{11} = - 5$

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

$100 - \frac{35 y}{11} = - 5$

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

$100 - \frac{35 y}{11} = - 5$

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

$100 - \frac{35 y}{11} = - 5$

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

Step 3

Solve for $y$ in $100 - \frac{35 y}{11} = - 5$ .

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Step 3.1

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

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Step 3.1.1

Subtract $100$ from both sides of the equation.

$- \frac{35 y}{11} = - 5 - 100$

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

Step 3.1.2

Subtract $100$ from $- 5$ .

$- \frac{35 y}{11} = - 105$

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

$- \frac{35 y}{11} = - 105$

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

Step 3.2

Multiply both sides of the equation by $- \frac{11}{35}$ .

$- \frac{11}{35} \cdot (- \frac{35 y}{11}) = - \frac{11}{35} \cdot - 105$

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

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $- \frac{11}{35} (- \frac{35 y}{11})$ .

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Step 3.3.1.1.1

Cancel the common factor of $11$ .

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Step 3.3.1.1.1.1

Move the leading negative in $- \frac{11}{35}$ into the numerator.

$\frac{- 11}{35} \cdot (- \frac{35 y}{11}) = - \frac{11}{35} \cdot - 105$

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

Step 3.3.1.1.1.2

Move the leading negative in $- \frac{35 y}{11}$ into the numerator.

$\frac{- 11}{35} \cdot \frac{- 35 y}{11} = - \frac{11}{35} \cdot - 105$

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

Step 3.3.1.1.1.3

Factor $11$ out of $- 11$ .

$\frac{11 (- 1)}{35} \cdot \frac{- 35 y}{11} = - \frac{11}{35} \cdot - 105$

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

Step 3.3.1.1.1.4

Cancel the common factor.

$\frac{11 \cdot - 1}{35} \cdot \frac{- 35 y}{11} = - \frac{11}{35} \cdot - 105$

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

Step 3.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{35} \cdot (- 35 y) = - \frac{11}{35} \cdot - 105$

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

$\frac{- 1}{35} \cdot (- 35 y) = - \frac{11}{35} \cdot - 105$

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

Step 3.3.1.1.2

Cancel the common factor of $35$ .

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Step 3.3.1.1.2.1

Factor $35$ out of $- 35 y$ .

$\frac{- 1}{35} \cdot (35 (- y)) = - \frac{11}{35} \cdot - 105$

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

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{35} \cdot (35 (- y)) = - \frac{11}{35} \cdot - 105$

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

Step 3.3.1.1.2.3

Rewrite the expression.

$y = - \frac{11}{35} \cdot - 105$

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

$y = - \frac{11}{35} \cdot - 105$

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

Step 3.3.1.1.3

Multiply.

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Step 3.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{11}{35} \cdot - 105$

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

Step 3.3.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{11}{35} \cdot - 105$

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

$y = - \frac{11}{35} \cdot - 105$

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

$y = - \frac{11}{35} \cdot - 105$

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

$y = - \frac{11}{35} \cdot - 105$

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

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $- \frac{11}{35} \cdot - 105$ .

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Step 3.3.2.1.1

Cancel the common factor of $35$ .

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Step 3.3.2.1.1.1

Move the leading negative in $- \frac{11}{35}$ into the numerator.

$y = \frac{- 11}{35} \cdot - 105$

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

Step 3.3.2.1.1.2

Factor $35$ out of $- 105$ .

$y = \frac{- 11}{35} \cdot (35 (- 3))$

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

Step 3.3.2.1.1.3

Cancel the common factor.

$y = \frac{- 11}{35} \cdot (35 \cdot - 3)$

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

Step 3.3.2.1.1.4

Rewrite the expression.

$y = - 11 \cdot - 3$

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

$y = - 11 \cdot - 3$

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

Step 3.3.2.1.2

Multiply $- 11$ by $- 3$ .

$y = 33$

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

$y = 33$

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

$y = 33$

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

$y = 33$

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

$y = 33$

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

Step 4

Replace all occurrences of $y$ with $33$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 50 - \frac{y}{11}$ with $33$ .

$x = 50 - \frac{33}{11}$

$y = 33$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $50 - \frac{33}{11}$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Divide $33$ by $11$ .

$x = 50 - 1 \cdot 3$

$y = 33$

Step 4.2.1.1.2

Multiply $- 1$ by $3$ .

$x = 50 - 3$

$y = 33$

$x = 50 - 3$

$y = 33$

Step 4.2.1.2

Subtract $3$ from $50$ .

$x = 47$

$y = 33$

$x = 47$

$y = 33$

$x = 47$

$y = 33$

$x = 47$

$y = 33$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(47, 33)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(47, 33)$

Equation Form:

$x = 47, y = 33$

Step 7