Find Three Ordered Pair Solutions 2x-3y=21

$2 x - 3 y = 21$

Step 1

Solve the equation for $y$ .

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

$- 3 y = 21 - 2 x$

Divide each term in $- 3 y = 21 - 2 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 21 - 2 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{21}{- 3} + \frac{- 2 x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{21}{- 3} + \frac{- 2 x}{- 3}$

Divide $y$ by $1$ .

$y = \frac{21}{- 3} + \frac{- 2 x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $21$ by $- 3$ .

$y = - 7 + \frac{- 2 x}{- 3}$

Dividing two negative values results in a positive value.

$y = - 7 + \frac{2 x}{3}$

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.

$y = - 7 + \frac{2 (0)}{3}$

Simplify $- 7 + \frac{2 (0)}{3}$ .

Multiply $2$ by $0$ .

$y = - 7 + \frac{0}{3}$

Divide $0$ by $3$ .

$y = - 7 + 0$

Add $- 7$ and $0$ .

$y = - 7$

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

$(0, - 7)$

Step 4

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

Remove parentheses.

$y = - 7 + \frac{2 (1)}{3}$

Simplify $- 7 + \frac{2 (1)}{3}$ .

Multiply $2$ by $1$ .

$y = - 7 + \frac{2}{3}$

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - 7 \cdot \frac{3}{3} + \frac{2}{3}$

Combine $- 7$ and $\frac{3}{3}$ .

$y = \frac{- 7 \cdot 3}{3} + \frac{2}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 7 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $- 7$ by $3$ .

$y = \frac{- 21 + 2}{3}$

Add $- 21$ and $2$ .

$y = \frac{- 19}{3}$

Move the negative in front of the fraction.

$y = - \frac{19}{3}$

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

$(1, - \frac{19}{3})$

Step 5

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

Remove parentheses.

$y = - 7 + \frac{2 (2)}{3}$

Simplify $- 7 + \frac{2 (2)}{3}$ .

Multiply $2$ by $2$ .

$y = - 7 + \frac{4}{3}$

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - 7 \cdot \frac{3}{3} + \frac{4}{3}$

Combine $- 7$ and $\frac{3}{3}$ .

$y = \frac{- 7 \cdot 3}{3} + \frac{4}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 7 \cdot 3 + 4}{3}$

Simplify the numerator.

Multiply $- 7$ by $3$ .

$y = \frac{- 21 + 4}{3}$

Add $- 21$ and $4$ .

$y = \frac{- 17}{3}$

Move the negative in front of the fraction.

$y = - \frac{17}{3}$

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

$(2, - \frac{17}{3})$

Step 6

These are three possible solutions to the equation.

$(0, - 7), (1, - \frac{19}{3}), (2, - \frac{17}{3})$

Step 7

Find Three Ordered Pair Solutions 2x-3y=21

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