Find Three Ordered Pair Solutions x=3y+1

$x = 3 y + 1$

Step 1

Solve the equation for $y$ .

Rewrite the equation as $3 y + 1 = x$ .

$3 y + 1 = x$

Subtract $1$ from both sides of the equation.

$3 y = x - 1$

Divide each term in $3 y = x - 1$ by $3$ and simplify.

Divide each term in $3 y = x - 1$ by $3$ .

$\frac{3 y}{3} = \frac{x}{3} + \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{x}{3} + \frac{- 1}{3}$

Divide $y$ by $1$ .

$y = \frac{x}{3} + \frac{- 1}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{x}{3} - \frac{1}{3}$

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.

$y = \frac{0}{3} - \frac{1}{3}$

Simplify $\frac{0}{3} - \frac{1}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{0 - 1}{3}$

Subtract $1$ from $0$ .

$y = \frac{- 1}{3}$

Move the negative in front of the fraction.

$y = - \frac{1}{3}$

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

$(0, - \frac{1}{3})$

Step 4

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

Remove parentheses.

$y = \frac{1}{3} - \frac{1}{3}$

Simplify $\frac{1}{3} - \frac{1}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{1 - 1}{3}$

Simplify the expression.

Subtract $1$ from $1$ .

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

Divide $0$ by $3$ .

$y = 0$

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

$(1, 0)$

Step 5

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

Remove parentheses.

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

Simplify $\frac{2}{3} - \frac{1}{3}$ .

Combine the numerators over the common denominator.

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

Subtract $1$ from $2$ .

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

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

$(2, \frac{1}{3})$

Step 6

These are three possible solutions to the equation.

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

Step 7

Find Three Ordered Pair Solutions x=3y+1

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