Find Three Ordered Pair Solutions 15x-12y=16

$15 x - 12 y = 16$

Step 1

Solve the equation for $y$ .

Subtract $15 x$ from both sides of the equation.

$- 12 y = 16 - 15 x$

Divide each term in $- 12 y = 16 - 15 x$ by $- 12$ and simplify.

Divide each term in $- 12 y = 16 - 15 x$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{16}{- 12} + \frac{- 15 x}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{16}{- 12} + \frac{- 15 x}{- 12}$

Divide $y$ by $1$ .

$y = \frac{16}{- 12} + \frac{- 15 x}{- 12}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $16$ and $- 12$ .

Factor $4$ out of $16$ .

$y = \frac{4 (4)}{- 12} + \frac{- 15 x}{- 12}$

Cancel the common factors.

Factor $4$ out of $- 12$ .

$y = \frac{4 \cdot 4}{4 \cdot - 3} + \frac{- 15 x}{- 12}$

Cancel the common factor.

$y = \frac{4 \cdot 4}{4 \cdot - 3} + \frac{- 15 x}{- 12}$

Rewrite the expression.

$y = \frac{4}{- 3} + \frac{- 15 x}{- 12}$

Move the negative in front of the fraction.

$y = - \frac{4}{3} + \frac{- 15 x}{- 12}$

Cancel the common factor of $- 15$ and $- 12$ .

Factor $- 3$ out of $- 15 x$ .

$y = - \frac{4}{3} + \frac{- 3 (5 x)}{- 12}$

Cancel the common factors.

Factor $- 3$ out of $- 12$ .

$y = - \frac{4}{3} + \frac{- 3 (5 x)}{- 3 (4)}$

Cancel the common factor.

$y = - \frac{4}{3} + \frac{- 3 (5 x)}{- 3 \cdot 4}$

Rewrite the expression.

$y = - \frac{4}{3} + \frac{5 x}{4}$

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.

Remove parentheses.

$y = - \frac{4}{3} + \frac{5 (0)}{4}$

Simplify $- \frac{4}{3} + \frac{5 (0)}{4}$ .

Multiply $5$ by $0$ .

$y = - \frac{4}{3} + \frac{0}{4}$

Divide $0$ by $4$ .

$y = - \frac{4}{3} + 0$

Add $- \frac{4}{3}$ and $0$ .

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

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

$(0, - \frac{4}{3})$

Step 4

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

Remove parentheses.

$y = - \frac{4}{3} + \frac{5 (1)}{4}$

Simplify $- \frac{4}{3} + \frac{5 (1)}{4}$ .

Multiply $5$ by $1$ .

$y = - \frac{4}{3} + \frac{5}{4}$

To write $- \frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{4}{3} \cdot \frac{4}{4} + \frac{5}{4}$

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{4}{3} \cdot \frac{4}{4} + \frac{5}{4} \cdot \frac{3}{3}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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

$y = - \frac{4 \cdot 4}{3 \cdot 4} + \frac{5}{4} \cdot \frac{3}{3}$

Multiply $3$ by $4$ .

$y = - \frac{4 \cdot 4}{12} + \frac{5}{4} \cdot \frac{3}{3}$

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$y = - \frac{4 \cdot 4}{12} + \frac{5 \cdot 3}{4 \cdot 3}$

Multiply $4$ by $3$ .

$y = - \frac{4 \cdot 4}{12} + \frac{5 \cdot 3}{12}$

Combine the numerators over the common denominator.

$y = \frac{- 4 \cdot 4 + 5 \cdot 3}{12}$

Simplify the numerator.

Multiply $- 4$ by $4$ .

$y = \frac{- 16 + 5 \cdot 3}{12}$

Multiply $5$ by $3$ .

$y = \frac{- 16 + 15}{12}$

Add $- 16$ and $15$ .

$y = \frac{- 1}{12}$

Move the negative in front of the fraction.

$y = - \frac{1}{12}$

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

$(1, - \frac{1}{12})$

Step 5

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

Remove parentheses.

$y = - \frac{4}{3} + \frac{5 (2)}{4}$

Simplify $- \frac{4}{3} + \frac{5 (2)}{4}$ .

Multiply $5$ by $2$ .

$y = - \frac{4}{3} + \frac{10}{4}$

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$y = - \frac{4}{3} + \frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = - \frac{4}{3} + \frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$y = - \frac{4}{3} + \frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$y = - \frac{4}{3} + \frac{5}{2}$

To write $- \frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{4}{3} \cdot \frac{2}{2} + \frac{5}{2}$

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{4}{3} \cdot \frac{2}{2} + \frac{5}{2} \cdot \frac{3}{3}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$y = - \frac{4 \cdot 2}{3 \cdot 2} + \frac{5}{2} \cdot \frac{3}{3}$

Multiply $3$ by $2$ .

$y = - \frac{4 \cdot 2}{6} + \frac{5}{2} \cdot \frac{3}{3}$

Multiply $\frac{5}{2}$ by $\frac{3}{3}$ .

$y = - \frac{4 \cdot 2}{6} + \frac{5 \cdot 3}{2 \cdot 3}$

Multiply $2$ by $3$ .

$y = - \frac{4 \cdot 2}{6} + \frac{5 \cdot 3}{6}$

Combine the numerators over the common denominator.

$y = \frac{- 4 \cdot 2 + 5 \cdot 3}{6}$

Simplify the numerator.

Multiply $- 4$ by $2$ .

$y = \frac{- 8 + 5 \cdot 3}{6}$

Multiply $5$ by $3$ .

$y = \frac{- 8 + 15}{6}$

Add $- 8$ and $15$ .

$y = \frac{7}{6}$

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

$(2, \frac{7}{6})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{4}{3}), (1, - \frac{1}{12}), (2, \frac{7}{6})$

Step 7

Find Three Ordered Pair Solutions 15x-12y=16

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