Algebra Examples

$- 9 + 5 y = - 4 x$ $- 11 x = - 20 + 9 y$

Step 1

Divide each term in $- 11 x = - 20 + 9 y$ by $- 11$ and simplify.

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Step 1.1

Divide each term in $- 11 x = - 20 + 9 y$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{- 20}{- 11} + \frac{9 y}{- 11}$

$- 9 + 5 y = - 4 x$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $- 11$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{- 20}{- 11} + \frac{9 y}{- 11}$

$- 9 + 5 y = - 4 x$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 20}{- 11} + \frac{9 y}{- 11}$

$- 9 + 5 y = - 4 x$

$x = \frac{- 20}{- 11} + \frac{9 y}{- 11}$

$- 9 + 5 y = - 4 x$

$x = \frac{- 20}{- 11} + \frac{9 y}{- 11}$

$- 9 + 5 y = - 4 x$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Dividing two negative values results in a positive value.

$x = \frac{20}{11} + \frac{9 y}{- 11}$

$- 9 + 5 y = - 4 x$

Step 1.3.1.2

Move the negative in front of the fraction.

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + 5 y = - 4 x$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + 5 y = - 4 x$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + 5 y = - 4 x$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + 5 y = - 4 x$

Step 2

Replace all occurrences of $x$ with $\frac{20}{11} - \frac{9 y}{11}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 9 + 5 y = - 4 x$ with $\frac{20}{11} - \frac{9 y}{11}$ .

$- 9 + 5 y = - 4 (\frac{20}{11} - \frac{9 y}{11})$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- 4 (\frac{20}{11} - \frac{9 y}{11})$ .

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Step 2.2.1.1

Apply the distributive property.

$- 9 + 5 y = - 4 (\frac{20}{11}) - 4 (- \frac{9 y}{11})$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 2.2.1.2

Multiply $- 4 (\frac{20}{11})$ .

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Step 2.2.1.2.1

Combine $- 4$ and $\frac{20}{11}$ .

$- 9 + 5 y = \frac{- 4 \cdot 20}{11} - 4 (- \frac{9 y}{11})$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 2.2.1.2.2

Multiply $- 4$ by $20$ .

$- 9 + 5 y = \frac{- 80}{11} - 4 (- \frac{9 y}{11})$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + 5 y = \frac{- 80}{11} - 4 (- \frac{9 y}{11})$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 2.2.1.3

Multiply $- 4 (- \frac{9 y}{11})$ .

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Step 2.2.1.3.1

Multiply $- 1$ by $- 4$ .

$- 9 + 5 y = \frac{- 80}{11} + 4 (\frac{9 y}{11})$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 2.2.1.3.2

Combine $4$ and $\frac{9 y}{11}$ .

$- 9 + 5 y = \frac{- 80}{11} + \frac{4 (9 y)}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 2.2.1.3.3

Multiply $9$ by $4$ .

$- 9 + 5 y = \frac{- 80}{11} + \frac{36 y}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + 5 y = \frac{- 80}{11} + \frac{36 y}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 2.2.1.4

Move the negative in front of the fraction.

$- 9 + 5 y = - \frac{80}{11} + \frac{36 y}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + 5 y = - \frac{80}{11} + \frac{36 y}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + 5 y = - \frac{80}{11} + \frac{36 y}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + 5 y = - \frac{80}{11} + \frac{36 y}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3

Solve for $y$ in $- 9 + 5 y = - \frac{80}{11} + \frac{36 y}{11}$ .

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Step 3.1

Move all terms containing $y$ to the left side of the equation.

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Step 3.1.1

Subtract $\frac{36 y}{11}$ from both sides of the equation.

$- 9 + 5 y - \frac{36 y}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.1.2

To write $5 y$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$- 9 + 5 y \cdot \frac{11}{11} - \frac{36 y}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.1.3

Combine $5 y$ and $\frac{11}{11}$ .

$- 9 + \frac{5 y \cdot 11}{11} - \frac{36 y}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.1.4

Combine the numerators over the common denominator.

$- 9 + \frac{5 y \cdot 11 - 36 y}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

Factor $y$ out of $5 y \cdot 11 - 36 y$ .

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Step 3.1.5.1.1.1

Factor $y$ out of $5 y \cdot 11$ .

$- 9 + \frac{y (5 \cdot 11) - 36 y}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.1.5.1.1.2

Factor $y$ out of $- 36 y$ .

$- 9 + \frac{y (5 \cdot 11) + y \cdot - 36}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.1.5.1.1.3

Factor $y$ out of $y (5 \cdot 11) + y \cdot - 36$ .

$- 9 + \frac{y (5 \cdot 11 - 36)}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + \frac{y (5 \cdot 11 - 36)}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.1.5.1.2

Multiply $5$ by $11$ .

$- 9 + \frac{y (55 - 36)}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.1.5.1.3

Subtract $36$ from $55$ .

$- 9 + \frac{y \cdot 19}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + \frac{y \cdot 19}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.1.5.2

Move $19$ to the left of $y$ .

$- 9 + \frac{19 y}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + \frac{19 y}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$- 9 + \frac{19 y}{11} = - \frac{80}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.2

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

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Step 3.2.1

Add $9$ to both sides of the equation.

$\frac{19 y}{11} = - \frac{80}{11} + 9$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.2.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{19 y}{11} = - \frac{80}{11} + 9 \cdot \frac{11}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.2.3

Combine $9$ and $\frac{11}{11}$ .

$\frac{19 y}{11} = - \frac{80}{11} + \frac{9 \cdot 11}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.2.4

Combine the numerators over the common denominator.

$\frac{19 y}{11} = \frac{- 80 + 9 \cdot 11}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $9$ by $11$ .

$\frac{19 y}{11} = \frac{- 80 + 99}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.2.5.2

Add $- 80$ and $99$ .

$\frac{19 y}{11} = \frac{19}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$\frac{19 y}{11} = \frac{19}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$\frac{19 y}{11} = \frac{19}{11}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$19 y = 19$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.4

Divide each term in $19 y = 19$ by $19$ and simplify.

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Step 3.4.1

Divide each term in $19 y = 19$ by $19$ .

$\frac{19 y}{19} = \frac{19}{19}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $19$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{19 y}{19} = \frac{19}{19}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{19}{19}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$y = \frac{19}{19}$

$x = \frac{20}{11} - \frac{9 y}{11}$

$y = \frac{19}{19}$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $19$ by $19$ .

$y = 1$

$x = \frac{20}{11} - \frac{9 y}{11}$

$y = 1$

$x = \frac{20}{11} - \frac{9 y}{11}$

$y = 1$

$x = \frac{20}{11} - \frac{9 y}{11}$

$y = 1$

$x = \frac{20}{11} - \frac{9 y}{11}$

Step 4

Replace all occurrences of $y$ with $1$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = \frac{20}{11} - \frac{9 y}{11}$ with $1$ .

$x = \frac{20}{11} - \frac{9 (1)}{11}$

$y = 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{20}{11} - \frac{9 (1)}{11}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{20 - 9 \cdot 1}{11}$

$y = 1$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Multiply $- 9$ by $1$ .

$x = \frac{20 - 9}{11}$

$y = 1$

Step 4.2.1.2.2

Subtract $9$ from $20$ .

$x = \frac{11}{11}$

$y = 1$

Step 4.2.1.2.3

Divide $11$ by $11$ .

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

Step 5

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

$(1, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 1)$

Equation Form:

$x = 1, y = 1$

Step 7