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

$9 x + 2 y = 13$

Step 1

Solve the equation for $y$ .

Subtract $9 x$ from both sides of the equation.

$2 y = 13 - 9 x$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $- 9$ by $0$ .

$y = \frac{13 + 0}{2}$

Add $13$ and $0$ .

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

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

$(0, \frac{13}{2})$

Step 4

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

Remove parentheses.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $- 9$ by $1$ .

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

Subtract $9$ from $13$ .

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

Divide $4$ by $2$ .

$y = 2$

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

$(1, 2)$

Step 5

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

Remove parentheses.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $- 9$ by $2$ .

$y = \frac{13 - 18}{2}$

Subtract $18$ from $13$ .

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

Move the negative in front of the fraction.

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

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.

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

Step 7

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

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