Kiani is shopping at a bookstore with a budget of $60. Hardbacks cost $12 and paperbacks cost $5. Write a two-variable inequality and determine the constraints of the problem. Which of the following points represents a viable solution?(1 point) Responses (−2,6) left parenthesis negative 2 comma 6 right parenthesis (6,6) left parenthesis 6 comma 6 right parenthesis (2,4) left parenthesis 2 comma 4 right parenthesis (1,4.5)

Let \( x \) represent the number of hardbacks and \( y \) represent the number of paperbacks that Kiani buys.

The cost of the hardbacks is \( 12x \) and the cost of the paperbacks is \( 5y \). Given that Kiani has a budget of $60, the inequality representing this situation is:

\[ 12x + 5y \leq 60 \]

Next, there are additional constraints to consider:

1. Both \( x \) and \( y \) must be non-negative since Kiani cannot buy a negative number of books: \[ x \geq 0 \] \[ y \geq 0 \]

Now, we will analyze the given points to determine if they satisfy the inequality: \( 12x + 5y \leq 60 \).

1. Point (-2, 6): \[ 12(-2) + 5(6) = -24 + 30 = 6 \quad (\text{valid since } 6 \leq 60) \quad \text{but } x < 0 \] Not viable because \( x \) is negative.

2. Point (6, 6): \[ 12(6) + 5(6) = 72 + 30 = 102 \quad (\text{not valid since } 102 > 60) \] Not viable.

3. Point (2, 4): \[ 12(2) + 5(4) = 24 + 20 = 44 \quad (\text{valid since } 44 \leq 60) \] Viable solution.

4. Point (1, 4.5): \[ 12(1) + 5(4.5) = 12 + 22.5 = 34.5 \quad (\text{valid since } 34.5 \leq 60) \] Viable solution.

Thus, the viable solutions from the points given are \( (2, 4) \) and \( (1, 4.5) \). However, the question specifies to choose one point, and that point is:

\[ \boxed{(2, 4)} \]