Find Three Ordered Pair Solutions 3y=2x-1

$3 y = 2 x - 1$

Step 1

Divide each term in $3 y = 2 x - 1$ by $3$ and simplify.

Divide each term in $3 y = 2 x - 1$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $2$ by $0$ .

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

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.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $2$ by $1$ .

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

Subtract $1$ from $2$ .

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

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

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

Step 5

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

Remove parentheses.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $2$ by $2$ .

$y = \frac{4 - 1}{3}$

Subtract $1$ from $4$ .

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

Divide $3$ by $3$ .

$y = 1$

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

$(2, 1)$

Step 6

These are three possible solutions to the equation.

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

Step 7

Find Three Ordered Pair Solutions 3y=2x-1

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