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

$3 x = 2 y + 1$

Step 1

Solve the equation for $y$ .

Rewrite the equation as $2 y + 1 = 3 x$ .

$2 y + 1 = 3 x$

Subtract $1$ from both sides of the equation.

$2 y = 3 x - 1$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $3$ by $0$ .

$y = \frac{0 - 1}{2}$

Subtract $1$ from $0$ .

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

Move the negative in front of the fraction.

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

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

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

Step 4

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

Remove parentheses.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $3$ by $1$ .

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

Subtract $1$ from $3$ .

$y = \frac{2}{2}$

Divide $2$ by $2$ .

$y = 1$

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

$(1, 1)$

Step 5

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

Remove parentheses.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $3$ by $2$ .

$y = \frac{6 - 1}{2}$

Subtract $1$ from $6$ .

$y = \frac{5}{2}$

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

$(2, \frac{5}{2})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{1}{2}), (1, 1), (2, \frac{5}{2})$

Step 7

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

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