Find Three Ordered Pair Solutions 2x+9y=13

$2 x + 9 y = 13$

Step 1

Solve the equation for $y$ .

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

$9 y = 13 - 2 x$

Divide each term in $9 y = 13 - 2 x$ by $9$ and simplify.

Divide each term in $9 y = 13 - 2 x$ by $9$ .

$\frac{9 y}{9} = \frac{13}{9} + \frac{- 2 x}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{13}{9} + \frac{- 2 x}{9}$

Divide $y$ by $1$ .

$y = \frac{13}{9} + \frac{- 2 x}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{13}{9} - \frac{2 x}{9}$

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.

$y = \frac{13}{9} - \frac{2 (0)}{9}$

Simplify $\frac{13}{9} - \frac{2 (0)}{9}$ .

Combine the numerators over the common denominator.

$y = \frac{13 - 2 \cdot 0}{9}$

Simplify the expression.

Multiply $- 2$ by $0$ .

$y = \frac{13 + 0}{9}$

Add $13$ and $0$ .

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

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

$(0, \frac{13}{9})$

Step 4

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

Remove parentheses.

$y = \frac{13}{9} - \frac{2 (1)}{9}$

Simplify $\frac{13}{9} - \frac{2 (1)}{9}$ .

Combine the numerators over the common denominator.

$y = \frac{13 - 2 \cdot 1}{9}$

Simplify the expression.

Multiply $- 2$ by $1$ .

$y = \frac{13 - 2}{9}$

Subtract $2$ from $13$ .

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

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

$(1, \frac{11}{9})$

Step 5

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

Remove parentheses.

$y = \frac{13}{9} - \frac{2 (2)}{9}$

Simplify $\frac{13}{9} - \frac{2 (2)}{9}$ .

Combine the numerators over the common denominator.

$y = \frac{13 - 2 \cdot 2}{9}$

Simplify the expression.

Multiply $- 2$ by $2$ .

$y = \frac{13 - 4}{9}$

Subtract $4$ from $13$ .

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

Divide $9$ by $9$ .

$y = 1$

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

$(2, 1)$

Step 6

These are three possible solutions to the equation.

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

Step 7

Find Three Ordered Pair Solutions 2x+9y=13

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