Linear Equations

The correct answer is: (D): 2, -3

We are given the function , where and are integers. We also know that and . We are tasked with finding the values of and .

Step 1: Use the information for

Substitute and into the function :

f(-1) = a(-1) + b = -5

This simplifies to:

-a + b = -5

Step 2: Use the information for

Next, substitute and into the function :

f(3) = a(3) + b = 3

This simplifies to:

3a + b = 3

Step 3: Solve the system of equations

We now have the system of equations:

-a + b = -5

3a + b = 3

To solve this system, subtract the first equation from the second equation:

(3a + b) - (-a + b) = 3 - (-5)

Simplifying this gives:

4a = 8

So, solving for , we get:

a = 2

Step 4: Solve for

Substitute into one of the original equations, say :

-2 + b = -5

Solving for , we get:

b = -3

Conclusion:
The values of and are and , so the correct answer is (D): 2, -3.

We need to evaluate the two statements given in the question:
Statement-I:
We are given two linear inequalities: 3x + 8 < 17 and 2x + 8 ≥ 12. Let's solve each inequality.
- Solve 3x + 8 < 17: 3x < 17 - 8 ⇒ 3x < 9 ⇒ x < 3. Thus, the solution to the first inequality is x < 3.

- Solve 2x + 8 ≥ 12: 2x ≥ 12 - 8 ⇒ 2x ≥ 4 ⇒ x ≥ 2. Thus, the solution to the second inequality is x ≥ 2.

Therefore, Statement-I is true since x < 3 and x ≥ 2 correctly represent the solution of the two inequalities.

Statement-II:
We need to check the common solution set for both inequalities.
From Statement-I, we know that: x < 3 and x ≥ 2. Thus, the common solution set should be x ∈ [2, 3), but Statement-II mentions x ∈ [2, 3], which is incorrect because x = 3 does not satisfy the inequality 3x + 8 < 17.

Hence, Statement-II is false. Thus, the correct answer is that Statement-I is true but Statement-II is false.