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

$- x + 3 y = 21$

Step 1

Solve the equation for $y$ .

Add $x$ to both sides of the equation.

$3 y = 21 + x$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $21$ by $3$ .

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

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.

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

Simplify $7 + \frac{0}{3}$ .

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.

$y = 7 + \frac{1}{3}$

Simplify $7 + \frac{1}{3}$ .

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

$y = 7 \cdot \frac{3}{3} + \frac{1}{3}$

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

$y = \frac{7 \cdot 3}{3} + \frac{1}{3}$

Combine the numerators over the common denominator.

$y = \frac{7 \cdot 3 + 1}{3}$

Simplify the numerator.

Multiply $7$ by $3$ .

$y = \frac{21 + 1}{3}$

Add $21$ and $1$ .

$y = \frac{22}{3}$

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

$(1, \frac{22}{3})$

Step 5

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

Remove parentheses.

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

Simplify $7 + \frac{2}{3}$ .

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 $2$ .

$y = \frac{23}{3}$

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

$(2, \frac{23}{3})$

Step 6

These are three possible solutions to the equation.

$(0, 7), (1, \frac{22}{3}), (2, \frac{23}{3})$

Step 7

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

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