Pre-Algebra Examples

$\frac{3}{4} x - 4 y = 2$

Step 1

Solve the equation for $y$ .

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Step 1.1

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} - 4 y = 2$

Step 1.2

Subtract $\frac{3 x}{4}$ from both sides of the equation.

$- 4 y = 2 - \frac{3 x}{4}$

Step 1.3

Divide each term in $- 4 y = 2 - \frac{3 x}{4}$ by $- 4$ and simplify.

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Step 1.3.1

Divide each term in $- 4 y = 2 - \frac{3 x}{4}$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{2}{- 4} + \frac{- \frac{3 x}{4}}{- 4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{2}{- 4} + \frac{- \frac{3 x}{4}}{- 4}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{2}{- 4} + \frac{- \frac{3 x}{4}}{- 4}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Cancel the common factor of $2$ and $- 4$ .

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Step 1.3.3.1.1.1

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{- 4} + \frac{- \frac{3 x}{4}}{- 4}$

Step 1.3.3.1.1.2

Cancel the common factors.

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Step 1.3.3.1.1.2.1

Factor $2$ out of $- 4$ .

$y = \frac{2 \cdot 1}{2 \cdot - 2} + \frac{- \frac{3 x}{4}}{- 4}$

Step 1.3.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot - 2} + \frac{- \frac{3 x}{4}}{- 4}$

Step 1.3.3.1.1.2.3

Rewrite the expression.

$y = \frac{1}{- 2} + \frac{- \frac{3 x}{4}}{- 4}$

Step 1.3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{1}{2} + \frac{- \frac{3 x}{4}}{- 4}$

Step 1.3.3.1.3

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{1}{2} - \frac{3 x}{4} \cdot \frac{1}{- 4}$

Step 1.3.3.1.4

Move the negative in front of the fraction.

$y = - \frac{1}{2} - \frac{3 x}{4} (- \frac{1}{4})$

Step 1.3.3.1.5

Multiply $- \frac{3 x}{4} (- \frac{1}{4})$ .

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Step 1.3.3.1.5.1

Multiply $- 1$ by $- 1$ .

$y = - \frac{1}{2} + 1 \frac{3 x}{4} \frac{1}{4}$

Step 1.3.3.1.5.2

Multiply $\frac{3 x}{4}$ by $1$ .

$y = - \frac{1}{2} + \frac{3 x}{4} \cdot \frac{1}{4}$

Step 1.3.3.1.5.3

Multiply $\frac{3 x}{4}$ by $\frac{1}{4}$ .

$y = - \frac{1}{2} + \frac{3 x}{4 \cdot 4}$

Step 1.3.3.1.5.4

Multiply $4$ by $4$ .

$y = - \frac{1}{2} + \frac{3 x}{16}$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

$y = - \frac{1}{2} + \frac{3 (0)}{16}$

Step 3.2

Simplify $- \frac{1}{2} + \frac{3 (0)}{16}$ .

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Step 3.2.1

Multiply $3$ by $0$ .

$y = - \frac{1}{2} + \frac{0}{16}$

Step 3.2.2

Divide $0$ by $16$ .

$y = - \frac{1}{2} + 0$

Step 3.2.3

Add $- \frac{1}{2}$ and $0$ .

$y = - \frac{1}{2}$

Step 3.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, - \frac{1}{2})$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = - \frac{1}{2} + \frac{3 (1)}{16}$

Step 4.2

Simplify $- \frac{1}{2} + \frac{3 (1)}{16}$ .

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Step 4.2.1

Multiply $3$ by $1$ .

$y = - \frac{1}{2} + \frac{3}{16}$

Step 4.2.2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = - \frac{1}{2} \cdot \frac{8}{8} + \frac{3}{16}$

Step 4.2.3

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.3.1

Multiply $\frac{1}{2}$ by $\frac{8}{8}$ .

$y = - \frac{8}{2 \cdot 8} + \frac{3}{16}$

Step 4.2.3.2

Multiply $2$ by $8$ .

$y = - \frac{8}{16} + \frac{3}{16}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{- 8 + 3}{16}$

Step 4.2.5

Add $- 8$ and $3$ .

$y = \frac{- 5}{16}$

Step 4.2.6

Move the negative in front of the fraction.

$y = - \frac{5}{16}$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, - \frac{5}{16})$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = - \frac{1}{2} + \frac{3 (2)}{16}$

Step 5.2

Simplify $- \frac{1}{2} + \frac{3 (2)}{16}$ .

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Step 5.2.1

Multiply $3$ by $2$ .

$y = - \frac{1}{2} + \frac{6}{16}$

Step 5.2.2

Cancel the common factor of $6$ and $16$ .

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Step 5.2.2.1

Factor $2$ out of $6$ .

$y = - \frac{1}{2} + \frac{2 (3)}{16}$

Step 5.2.2.2

Cancel the common factors.

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Step 5.2.2.2.1

Factor $2$ out of $16$ .

$y = - \frac{1}{2} + \frac{2 \cdot 3}{2 \cdot 8}$

Step 5.2.2.2.2

Cancel the common factor.

$y = - \frac{1}{2} + \frac{2 \cdot 3}{2 \cdot 8}$

Step 5.2.2.2.3

Rewrite the expression.

$y = - \frac{1}{2} + \frac{3}{8}$

Step 5.2.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{1}{2} \cdot \frac{4}{4} + \frac{3}{8}$

Step 5.2.4

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.2.4.1

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$y = - \frac{4}{2 \cdot 4} + \frac{3}{8}$

Step 5.2.4.2

Multiply $2$ by $4$ .

$y = - \frac{4}{8} + \frac{3}{8}$

Step 5.2.5

Combine the numerators over the common denominator.

$y = \frac{- 4 + 3}{8}$

Step 5.2.6

Add $- 4$ and $3$ .

$y = \frac{- 1}{8}$

Step 5.2.7

Move the negative in front of the fraction.

$y = - \frac{1}{8}$

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, - \frac{1}{8})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{1}{2}), (1, - \frac{5}{16}), (2, - \frac{1}{8})$

Step 7