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

$3 x - 2 y = - 1$

Step 1

Solve the equation for $y$ .

Subtract $3 x$ from both sides of the equation.

$- 2 y = - 1 - 3 x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

Dividing two negative values results in a positive value.

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

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.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $3$ by $0$ .

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

Add $1$ and $0$ .

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

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.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $3$ by $1$ .

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

Add $1$ and $3$ .

$y = \frac{4}{2}$

Divide $4$ by $2$ .

$y = 2$

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

$(1, 2)$

Step 5

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

Remove parentheses.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $3$ by $2$ .

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

Add $1$ and $6$ .

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

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

$(2, \frac{7}{2})$

Step 6

These are three possible solutions to the equation.

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

Step 7

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

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