Question Statement:
The system of equations for the variables x and y a x+by=e cx+d y= f has a unique solution only if
Options:
-
(A) ad -be # 0
-
(B) ac-bd # 0
-
(C) a+c#b+d
-
(D) a -c#b-d
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2015 Q.9)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (2 Mark, MCQ)
- **Topic**: Verbal Aptitude (Verbal Deduction & Reasoning)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> The system of equations for the variables x and y a x+by=e cx+d y= f has a unique solution only if
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Verbal Aptitude** (Verbal Deduction & Reasoning) under *General Aptitude*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"ad -be # 0"*: ❌ **INCORRECT**.
- **(B)** *"ac-bd # 0"*: ❌ **INCORRECT**.
- **(C)** *"a+c#b+d"*: ✅ **CORRECT**.
- **(D)** *"a -c#b-d"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2015 (IIT Kanpur) master answer key with 100% precision.
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