Find Three Ordered Pair Solutions 2x+3y=16

$2 x + 3 y = 16$

Step 1

Solve the equation for $y$ .

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

$3 y = 16 - 2 x$

Divide each term in $3 y = 16 - 2 x$ by $3$ and simplify.

Divide each term in $3 y = 16 - 2 x$ by $3$ .

$\frac{3 y}{3} = \frac{16}{3} + \frac{- 2 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{16}{3} + \frac{- 2 x}{3}$

Divide $y$ by $1$ .

$y = \frac{16}{3} + \frac{- 2 x}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{16}{3} - \frac{2 x}{3}$

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.

$y = \frac{16}{3} - \frac{2 (0)}{3}$

Simplify $\frac{16}{3} - \frac{2 (0)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{16 - 2 \cdot 0}{3}$

Simplify the expression.

Multiply $- 2$ by $0$ .

$y = \frac{16 + 0}{3}$

Add $16$ and $0$ .

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

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

$(0, \frac{16}{3})$

Step 4

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

Remove parentheses.

$y = \frac{16}{3} - \frac{2 (1)}{3}$

Simplify $\frac{16}{3} - \frac{2 (1)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{16 - 2 \cdot 1}{3}$

Simplify the expression.

Multiply $- 2$ by $1$ .

$y = \frac{16 - 2}{3}$

Subtract $2$ from $16$ .

$y = \frac{14}{3}$

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

$(1, \frac{14}{3})$

Step 5

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

Remove parentheses.

$y = \frac{16}{3} - \frac{2 (2)}{3}$

Simplify $\frac{16}{3} - \frac{2 (2)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{16 - 2 \cdot 2}{3}$

Simplify the expression.

Multiply $- 2$ by $2$ .

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

Subtract $4$ from $16$ .

$y = \frac{12}{3}$

Divide $12$ by $3$ .

$y = 4$

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

$(2, 4)$

Step 6

These are three possible solutions to the equation.

$(0, \frac{16}{3}), (1, \frac{14}{3}), (2, 4)$

Step 7

Find Three Ordered Pair Solutions 2x+3y=16

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