Find Three Ordered Pair Solutions 2x-9y=15

$2 x - 9 y = 15$

Step 1

Solve the equation for $y$ .

Subtract $2 x$ from both sides of the equation.

$- 9 y = 15 - 2 x$

Divide each term in $- 9 y = 15 - 2 x$ by $- 9$ and simplify.

Divide each term in $- 9 y = 15 - 2 x$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{15}{- 9} + \frac{- 2 x}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{15}{- 9} + \frac{- 2 x}{- 9}$

Divide $y$ by $1$ .

$y = \frac{15}{- 9} + \frac{- 2 x}{- 9}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $15$ and $- 9$ .

Factor $3$ out of $15$ .

$y = \frac{3 (5)}{- 9} + \frac{- 2 x}{- 9}$

Cancel the common factors.

Factor $3$ out of $- 9$ .

$y = \frac{3 \cdot 5}{3 \cdot - 3} + \frac{- 2 x}{- 9}$

Cancel the common factor.

$y = \frac{3 \cdot 5}{3 \cdot - 3} + \frac{- 2 x}{- 9}$

Rewrite the expression.

$y = \frac{5}{- 3} + \frac{- 2 x}{- 9}$

Move the negative in front of the fraction.

$y = - \frac{5}{3} + \frac{- 2 x}{- 9}$

Dividing two negative values results in a positive value.

$y = - \frac{5}{3} + \frac{2 x}{9}$

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.

$y = - \frac{5}{3} + \frac{2 (0)}{9}$

Simplify $- \frac{5}{3} + \frac{2 (0)}{9}$ .

Multiply $2$ by $0$ .

$y = - \frac{5}{3} + \frac{0}{9}$

Divide $0$ by $9$ .

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

Add $- \frac{5}{3}$ and $0$ .

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

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

$(0, - \frac{5}{3})$

Step 4

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

Remove parentheses.

$y = - \frac{5}{3} + \frac{2 (1)}{9}$

Simplify $- \frac{5}{3} + \frac{2 (1)}{9}$ .

Multiply $2$ by $1$ .

$y = - \frac{5}{3} + \frac{2}{9}$

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

$y = - \frac{5}{3} \cdot \frac{3}{3} + \frac{2}{9}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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

$y = - \frac{5 \cdot 3}{3 \cdot 3} + \frac{2}{9}$

Multiply $3$ by $3$ .

$y = - \frac{5 \cdot 3}{9} + \frac{2}{9}$

Combine the numerators over the common denominator.

$y = \frac{- 5 \cdot 3 + 2}{9}$

Simplify the numerator.

Multiply $- 5$ by $3$ .

$y = \frac{- 15 + 2}{9}$

Add $- 15$ and $2$ .

$y = \frac{- 13}{9}$

Move the negative in front of the fraction.

$y = - \frac{13}{9}$

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

$(1, - \frac{13}{9})$

Step 5

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

Remove parentheses.

$y = - \frac{5}{3} + \frac{2 (2)}{9}$

Simplify $- \frac{5}{3} + \frac{2 (2)}{9}$ .

Multiply $2$ by $2$ .

$y = - \frac{5}{3} + \frac{4}{9}$

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

$y = - \frac{5}{3} \cdot \frac{3}{3} + \frac{4}{9}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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

$y = - \frac{5 \cdot 3}{3 \cdot 3} + \frac{4}{9}$

Multiply $3$ by $3$ .

$y = - \frac{5 \cdot 3}{9} + \frac{4}{9}$

Combine the numerators over the common denominator.

$y = \frac{- 5 \cdot 3 + 4}{9}$

Simplify the numerator.

Multiply $- 5$ by $3$ .

$y = \frac{- 15 + 4}{9}$

Add $- 15$ and $4$ .

$y = \frac{- 11}{9}$

Move the negative in front of the fraction.

$y = - \frac{11}{9}$

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

$(2, - \frac{11}{9})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{5}{3}), (1, - \frac{13}{9}), (2, - \frac{11}{9})$

Step 7

Find Three Ordered Pair Solutions 2x-9y=15

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