Algebra Examples

$5 x - 9 y = 6$ $- (5 x + 2 y) = (17)$

Step 1

Solve for $x$ in $5 x - 9 y = 6$ .

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Step 1.1

Add $9 y$ to both sides of the equation.

$5 x = 6 + 9 y$

$- 5 x - 2 y = 17$

Step 1.2

Divide each term in $5 x = 6 + 9 y$ by $5$ and simplify.

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Step 1.2.1

Divide each term in $5 x = 6 + 9 y$ by $5$ .

$\frac{5 x}{5} = \frac{6}{5} + \frac{9 y}{5}$

$- 5 x - 2 y = 17$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{6}{5} + \frac{9 y}{5}$

$- 5 x - 2 y = 17$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 5 x - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 5 x - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 5 x - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 5 x - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 5 x - 2 y = 17$

Step 2

Replace all occurrences of $x$ with $\frac{6}{5} + \frac{9 y}{5}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 5 x - 2 y = 17$ with $\frac{6}{5} + \frac{9 y}{5}$ .

$- 5 (\frac{6}{5} + \frac{9 y}{5}) - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 5 (\frac{6}{5} + \frac{9 y}{5}) - 2 y$ .

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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.

$- 5 (\frac{6}{5}) - 5 \frac{9 y}{5} - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 2.2.1.1.2

Cancel the common factor of $5$ .

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Step 2.2.1.1.2.1

Factor $5$ out of $- 5$ .

$5 (- 1) (\frac{6}{5}) - 5 \frac{9 y}{5} - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 2.2.1.1.2.2

Cancel the common factor.

$5 \cdot (- 1 (\frac{6}{5})) - 5 \frac{9 y}{5} - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 2.2.1.1.2.3

Rewrite the expression.

$- 1 \cdot 6 - 5 \frac{9 y}{5} - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 1 \cdot 6 - 5 \frac{9 y}{5} - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 2.2.1.1.3

Multiply $- 1$ by $6$ .

$- 6 - 5 \frac{9 y}{5} - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 2.2.1.1.4

Cancel the common factor of $5$ .

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Step 2.2.1.1.4.1

Factor $5$ out of $- 5$ .

$- 6 + 5 (- 1) (\frac{9 y}{5}) - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 2.2.1.1.4.2

Cancel the common factor.

$- 6 + 5 \cdot (- 1 \frac{9 y}{5}) - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 2.2.1.1.4.3

Rewrite the expression.

$- 6 - 1 (9 y) - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 6 - 1 (9 y) - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 2.2.1.1.5

Multiply $9$ by $- 1$ .

$- 6 - 9 y - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 6 - 9 y - 2 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 2.2.1.2

Subtract $2 y$ from $- 9 y$ .

$- 6 - 11 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 6 - 11 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 6 - 11 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 6 - 11 y = 17$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 3

Solve for $y$ in $- 6 - 11 y = 17$ .

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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

Add $6$ to both sides of the equation.

$- 11 y = 17 + 6$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 3.1.2

Add $17$ and $6$ .

$- 11 y = 23$

$x = \frac{6}{5} + \frac{9 y}{5}$

$- 11 y = 23$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 3.2

Divide each term in $- 11 y = 23$ by $- 11$ and simplify.

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Step 3.2.1

Divide each term in $- 11 y = 23$ by $- 11$ .

$\frac{- 11 y}{- 11} = \frac{23}{- 11}$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 11$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 11 y}{- 11} = \frac{23}{- 11}$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{23}{- 11}$

$x = \frac{6}{5} + \frac{9 y}{5}$

$y = \frac{23}{- 11}$

$x = \frac{6}{5} + \frac{9 y}{5}$

$y = \frac{23}{- 11}$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$y = - \frac{23}{11}$

$x = \frac{6}{5} + \frac{9 y}{5}$

$y = - \frac{23}{11}$

$x = \frac{6}{5} + \frac{9 y}{5}$

$y = - \frac{23}{11}$

$x = \frac{6}{5} + \frac{9 y}{5}$

$y = - \frac{23}{11}$

$x = \frac{6}{5} + \frac{9 y}{5}$

Step 4

Replace all occurrences of $y$ with $- \frac{23}{11}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = \frac{6}{5} + \frac{9 y}{5}$ with $- \frac{23}{11}$ .

$x = \frac{6}{5} + \frac{9 (- \frac{23}{11})}{5}$

$y = - \frac{23}{11}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{6}{5} + \frac{9 (- \frac{23}{11})}{5}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{6 + 9 (- \frac{23}{11})}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.2

Simplify each term.

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Step 4.2.1.2.1

Multiply $9 (- \frac{23}{11})$ .

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Step 4.2.1.2.1.1

Multiply $- 1$ by $9$ .

$x = \frac{6 - 9 (\frac{23}{11})}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.2.1.2

Combine $- 9$ and $\frac{23}{11}$ .

$x = \frac{6 + \frac{- 9 \cdot 23}{11}}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.2.1.3

Multiply $- 9$ by $23$ .

$x = \frac{6 + \frac{- 207}{11}}{5}$

$y = - \frac{23}{11}$

$x = \frac{6 + \frac{- 207}{11}}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.2.2

Move the negative in front of the fraction.

$x = \frac{6 - \frac{207}{11}}{5}$

$y = - \frac{23}{11}$

$x = \frac{6 - \frac{207}{11}}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.3

To write $6$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x = \frac{6 \cdot \frac{11}{11} - \frac{207}{11}}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.4

Combine $6$ and $\frac{11}{11}$ .

$x = \frac{\frac{6 \cdot 11}{11} - \frac{207}{11}}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.5

Combine the numerators over the common denominator.

$x = \frac{\frac{6 \cdot 11 - 207}{11}}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.6

Simplify the numerator.

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Step 4.2.1.6.1

Multiply $6$ by $11$ .

$x = \frac{\frac{66 - 207}{11}}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.6.2

Subtract $207$ from $66$ .

$x = \frac{\frac{- 141}{11}}{5}$

$y = - \frac{23}{11}$

$x = \frac{\frac{- 141}{11}}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.7

Move the negative in front of the fraction.

$x = \frac{- \frac{141}{11}}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.8

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{141}{11} \cdot \frac{1}{5}$

$y = - \frac{23}{11}$

Step 4.2.1.9

Multiply $- \frac{141}{11} \cdot \frac{1}{5}$ .

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Step 4.2.1.9.1

Multiply $\frac{1}{5}$ by $\frac{141}{11}$ .

$x = - \frac{141}{5 \cdot 11}$

$y = - \frac{23}{11}$

Step 4.2.1.9.2

Multiply $5$ by $11$ .

$x = - \frac{141}{55}$

$y = - \frac{23}{11}$

$x = - \frac{141}{55}$

$y = - \frac{23}{11}$

$x = - \frac{141}{55}$

$y = - \frac{23}{11}$

$x = - \frac{141}{55}$

$y = - \frac{23}{11}$

$x = - \frac{141}{55}$

$y = - \frac{23}{11}$

Step 5

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

$(- \frac{141}{55}, - \frac{23}{11})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{141}{55}, - \frac{23}{11})$

Equation Form:

$x = - \frac{141}{55}, y = - \frac{23}{11}$

Step 7