Algebra Examples

$- 16 + 20 x - 8 y = 0$ $36 = - 18 y - 22 x$

Step 1

Solve for $x$ in $- 16 + 20 x - 8 y = 0$ .

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Step 1.1

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

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Step 1.1.1

Add $16$ to both sides of the equation.

$20 x - 8 y = 16$

$36 = - 18 y - 22 x$

Step 1.1.2

Add $8 y$ to both sides of the equation.

$20 x = 16 + 8 y$

$36 = - 18 y - 22 x$

$20 x = 16 + 8 y$

$36 = - 18 y - 22 x$

Step 1.2

Divide each term in $20 x = 16 + 8 y$ by $20$ and simplify.

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Step 1.2.1

Divide each term in $20 x = 16 + 8 y$ by $20$ .

$\frac{20 x}{20} = \frac{16}{20} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $20$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{20 x}{20} = \frac{16}{20} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{16}{20} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

$x = \frac{16}{20} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

$x = \frac{16}{20} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Cancel the common factor of $16$ and $20$ .

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Step 1.2.3.1.1.1

Factor $4$ out of $16$ .

$x = \frac{4 (4)}{20} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $4$ out of $20$ .

$x = \frac{4 \cdot 4}{4 \cdot 5} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$x = \frac{4 \cdot 4}{4 \cdot 5} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$x = \frac{4}{5} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

$x = \frac{4}{5} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

$x = \frac{4}{5} + \frac{8 y}{20}$

$36 = - 18 y - 22 x$

Step 1.2.3.1.2

Cancel the common factor of $8$ and $20$ .

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Step 1.2.3.1.2.1

Factor $4$ out of $8 y$ .

$x = \frac{4}{5} + \frac{4 (2 y)}{20}$

$36 = - 18 y - 22 x$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $4$ out of $20$ .

$x = \frac{4}{5} + \frac{4 (2 y)}{4 (5)}$

$36 = - 18 y - 22 x$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = \frac{4}{5} + \frac{4 (2 y)}{4 \cdot 5}$

$36 = - 18 y - 22 x$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y - 22 x$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y - 22 x$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y - 22 x$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y - 22 x$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y - 22 x$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y - 22 x$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y - 22 x$

Step 2

Replace all occurrences of $x$ with $\frac{4}{5} + \frac{2 y}{5}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $36 = - 18 y - 22 x$ with $\frac{4}{5} + \frac{2 y}{5}$ .

$36 = - 18 y - 22 (\frac{4}{5} + \frac{2 y}{5})$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- 18 y - 22 (\frac{4}{5} + \frac{2 y}{5})$ .

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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.

$36 = - 18 y - 22 (\frac{4}{5}) - 22 \frac{2 y}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.2

Multiply $- 22 (\frac{4}{5})$ .

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Step 2.2.1.1.2.1

Combine $- 22$ and $\frac{4}{5}$ .

$36 = - 18 y + \frac{- 22 \cdot 4}{5} - 22 \frac{2 y}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.2.2

Multiply $- 22$ by $4$ .

$36 = - 18 y + \frac{- 88}{5} - 22 \frac{2 y}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y + \frac{- 88}{5} - 22 \frac{2 y}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.3

Multiply $- 22 \frac{2 y}{5}$ .

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Step 2.2.1.1.3.1

Combine $- 22$ and $\frac{2 y}{5}$ .

$36 = - 18 y + \frac{- 88}{5} + \frac{- 22 (2 y)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.3.2

Multiply $2$ by $- 22$ .

$36 = - 18 y + \frac{- 88}{5} + \frac{- 44 y}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y + \frac{- 88}{5} + \frac{- 44 y}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.4

Simplify each term.

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Step 2.2.1.1.4.1

Move the negative in front of the fraction.

$36 = - 18 y - \frac{88}{5} + \frac{- 44 y}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.1.4.2

Move the negative in front of the fraction.

$36 = - 18 y - \frac{88}{5} - \frac{44 y}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y - \frac{88}{5} - \frac{44 y}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - 18 y - \frac{88}{5} - \frac{44 y}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.2

To write $- 18 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$36 = - 18 y \cdot \frac{5}{5} - \frac{44 y}{5} - \frac{88}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.3

Combine $- 18 y$ and $\frac{5}{5}$ .

$36 = \frac{- 18 y \cdot 5}{5} - \frac{44 y}{5} - \frac{88}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.4

Combine the numerators over the common denominator.

$36 = \frac{- 18 y \cdot 5 - 44 y}{5} - \frac{88}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.5

Combine the numerators over the common denominator.

$36 = \frac{- 18 y \cdot 5 - 44 y - 88}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.6

Multiply $5$ by $- 18$ .

$36 = \frac{- 90 y - 44 y - 88}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.7

Subtract $44 y$ from $- 90 y$ .

$36 = \frac{- 134 y - 88}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.8

Factor $2$ out of $- 134 y - 88$ .

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Step 2.2.1.8.1

Factor $2$ out of $- 134 y$ .

$36 = \frac{2 (- 67 y) - 88}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.8.2

Factor $2$ out of $- 88$ .

$36 = \frac{2 (- 67 y) + 2 (- 44)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.8.3

Factor $2$ out of $2 (- 67 y) + 2 (- 44)$ .

$36 = \frac{2 (- 67 y - 44)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = \frac{2 (- 67 y - 44)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.9

Factor $- 1$ out of $- 67 y$ .

$36 = \frac{2 (- (67 y) - 44)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.10

Rewrite $- 44$ as $- 1 (44)$ .

$36 = \frac{2 (- (67 y) - 1 \cdot 44)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.11

Factor $- 1$ out of $- (67 y) - 1 (44)$ .

$36 = \frac{2 (- (67 y + 44))}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.12

Simplify the expression.

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Step 2.2.1.12.1

Rewrite $- (67 y + 44)$ as $- 1 (67 y + 44)$ .

$36 = \frac{2 (- 1 (67 y + 44))}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 2.2.1.12.2

Move the negative in front of the fraction.

$36 = - \frac{2 (67 y + 44)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - \frac{2 (67 y + 44)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - \frac{2 (67 y + 44)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - \frac{2 (67 y + 44)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$36 = - \frac{2 (67 y + 44)}{5}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3

Solve for $y$ in $36 = - \frac{2 (67 y + 44)}{5}$ .

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Step 3.1

Rewrite the equation as $- \frac{2 (67 y + 44)}{5} = 36$ .

$- \frac{2 (67 y + 44)}{5} = 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.2

Multiply both sides of the equation by $- \frac{5}{2}$ .

$- \frac{5}{2} \cdot (- \frac{2 (67 y + 44)}{5}) = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

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 $- \frac{5}{2} (- \frac{2 (67 y + 44)}{5})$ .

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Step 3.3.1.1.1

Cancel the common factor of $5$ .

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Step 3.3.1.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} \cdot (- \frac{2 (67 y + 44)}{5}) = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.1.1.1.2

Move the leading negative in $- \frac{2 (67 y + 44)}{5}$ into the numerator.

$\frac{- 5}{2} \cdot \frac{- 2 (67 y + 44)}{5} = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 (67 y + 44)}{5} = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 (67 y + 44)}{5} = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} \cdot (- 2 (67 y + 44)) = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

$\frac{- 1}{2} \cdot (- 2 (67 y + 44)) = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.1.1.2

Cancel the common factor of $2$ .

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Step 3.3.1.1.2.1

Factor $2$ out of $- 2 (67 y + 44)$ .

$\frac{- 1}{2} \cdot (2 (- (67 y + 44))) = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} \cdot (2 (- (67 y + 44))) = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.1.1.2.3

Rewrite the expression.

$67 y + 44 = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

$67 y + 44 = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.1.1.3

Multiply.

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Step 3.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 (67 y + 44) = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.1.1.3.2

Multiply $67 y + 44$ by $1$ .

$67 y + 44 = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

$67 y + 44 = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

$67 y + 44 = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

$67 y + 44 = - \frac{5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $- \frac{5}{2} \cdot 36$ .

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Step 3.3.2.1.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$67 y + 44 = \frac{- 5}{2} \cdot 36$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.2.1.1.2

Factor $2$ out of $36$ .

$67 y + 44 = \frac{- 5}{2} \cdot (2 (18))$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.2.1.1.3

Cancel the common factor.

$67 y + 44 = \frac{- 5}{2} \cdot (2 \cdot 18)$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.2.1.1.4

Rewrite the expression.

$67 y + 44 = - 5 \cdot 18$

$x = \frac{4}{5} + \frac{2 y}{5}$

$67 y + 44 = - 5 \cdot 18$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.3.2.1.2

Multiply $- 5$ by $18$ .

$67 y + 44 = - 90$

$x = \frac{4}{5} + \frac{2 y}{5}$

$67 y + 44 = - 90$

$x = \frac{4}{5} + \frac{2 y}{5}$

$67 y + 44 = - 90$

$x = \frac{4}{5} + \frac{2 y}{5}$

$67 y + 44 = - 90$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.4

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

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Step 3.4.1

Subtract $44$ from both sides of the equation.

$67 y = - 90 - 44$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.4.2

Subtract $44$ from $- 90$ .

$67 y = - 134$

$x = \frac{4}{5} + \frac{2 y}{5}$

$67 y = - 134$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.5

Divide each term in $67 y = - 134$ by $67$ and simplify.

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Step 3.5.1

Divide each term in $67 y = - 134$ by $67$ .

$\frac{67 y}{67} = \frac{- 134}{67}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.5.2

Simplify the left side.

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Step 3.5.2.1

Cancel the common factor of $67$ .

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Step 3.5.2.1.1

Cancel the common factor.

$\frac{67 y}{67} = \frac{- 134}{67}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 134}{67}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$y = \frac{- 134}{67}$

$x = \frac{4}{5} + \frac{2 y}{5}$

$y = \frac{- 134}{67}$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 3.5.3

Simplify the right side.

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Step 3.5.3.1

Divide $- 134$ by $67$ .

$y = - 2$

$x = \frac{4}{5} + \frac{2 y}{5}$

$y = - 2$

$x = \frac{4}{5} + \frac{2 y}{5}$

$y = - 2$

$x = \frac{4}{5} + \frac{2 y}{5}$

$y = - 2$

$x = \frac{4}{5} + \frac{2 y}{5}$

Step 4

Replace all occurrences of $y$ with $- 2$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = \frac{4}{5} + \frac{2 y}{5}$ with $- 2$ .

$x = \frac{4}{5} + \frac{2 (- 2)}{5}$

$y = - 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4}{5} + \frac{2 (- 2)}{5}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{4 + 2 (- 2)}{5}$

$y = - 2$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Multiply $2$ by $- 2$ .

$x = \frac{4 - 4}{5}$

$y = - 2$

Step 4.2.1.2.2

Subtract $4$ from $4$ .

$x = \frac{0}{5}$

$y = - 2$

Step 4.2.1.2.3

Divide $0$ by $5$ .

$x = 0$

$y = - 2$

$x = 0$

$y = - 2$

$x = 0$

$y = - 2$

$x = 0$

$y = - 2$

$x = 0$

$y = - 2$

Step 5

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

$(0, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, - 2)$

Equation Form:

$x = 0, y = - 2$

Step 7