Pre-Algebra Examples

$3 x - 4 y - 16 = 0$

Step 1

Solve the equation for $y$ .

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Step 1.1

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

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Step 1.1.1

Subtract $3 x$ from both sides of the equation.

$- 4 y - 16 = - 3 x$

Step 1.1.2

Add $16$ to both sides of the equation.

$- 4 y = - 3 x + 16$

Step 1.2

Divide each term in $- 4 y = - 3 x + 16$ by $- 4$ and simplify.

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Step 1.2.1

Divide each term in $- 4 y = - 3 x + 16$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 3 x}{- 4} + \frac{16}{- 4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 3 x}{- 4} + \frac{16}{- 4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 3 x}{- 4} + \frac{16}{- 4}$

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

Dividing two negative values results in a positive value.

$y = \frac{3 x}{4} + \frac{16}{- 4}$

Step 1.2.3.1.2

Divide $16$ by $- 4$ .

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

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.

$y = \frac{3 (0)}{4} - 4$

Step 3.2

Simplify $\frac{3 (0)}{4} - 4$ .

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Step 3.2.1

Multiply $3$ by $0$ .

$y = \frac{0}{4} - 4$

Step 3.2.2

Divide $0$ by $4$ .

$y = 0 - 4$

Step 3.2.3

Subtract $4$ from $0$ .

$y = - 4$

Step 3.3

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

$(0, - 4)$

Step 4

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

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Step 4.1

Remove parentheses.

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

Step 4.2

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

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Step 4.2.1

Multiply $3$ by $1$ .

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

Step 4.2.2

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

$y = \frac{3}{4} - 4 \cdot \frac{4}{4}$

Step 4.2.3

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

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

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{3 - 4 \cdot 4}{4}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $- 4$ by $4$ .

$y = \frac{3 - 16}{4}$

Step 4.2.5.2

Subtract $16$ from $3$ .

$y = \frac{- 13}{4}$

Step 4.2.6

Move the negative in front of the fraction.

$y = - \frac{13}{4}$

Step 4.3

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

$(1, - \frac{13}{4})$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

Simplify $\frac{3 (2)}{4} - 4$ .

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Step 5.2.1

Multiply $3$ by $2$ .

$y = \frac{6}{4} - 4$

Step 5.2.2

Cancel the common factor of $6$ and $4$ .

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Step 5.2.2.1

Factor $2$ out of $6$ .

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

Step 5.2.2.2

Cancel the common factors.

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Step 5.2.2.2.1

Factor $2$ out of $4$ .

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

Step 5.2.2.2.2

Cancel the common factor.

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

Step 5.2.2.2.3

Rewrite the expression.

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

Step 5.2.3

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

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

Step 5.2.4

Combine $- 4$ and $\frac{2}{2}$ .

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

Step 5.2.5

Combine the numerators over the common denominator.

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

Step 5.2.6

Simplify the numerator.

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Step 5.2.6.1

Multiply $- 4$ by $2$ .

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

Step 5.2.6.2

Subtract $8$ from $3$ .

$y = \frac{- 5}{2}$

Step 5.2.7

Move the negative in front of the fraction.

$y = - \frac{5}{2}$

Step 5.3

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

$(2, - \frac{5}{2})$

Step 6

These are three possible solutions to the equation.

$(0, - 4), (1, - \frac{13}{4}), (2, - \frac{5}{2})$

Step 7