Question Statement:
4. *D Question Number : 12 Question Type: MCQ 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:
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(A) ad -be # 0
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(B) ac-bd # 0
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(C) a+c#b+d
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(D) a -c#b-d
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2015 Q.9)**
**1. Governing Concept & Theory**:
This problem evaluates **Verbal Aptitude** within the General Aptitude module (2 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Linguistic / Mathematical Principle**: The problem statement requires contextual grammatical concord, semantic consistency, or logical deduction.
2. **Evaluation of Choices**: Analyzing the option set confirms that **(C)** (`a+c#b+d`) directly satisfies all relational, semantic, and structural criteria.
3. **Rejection of Distractors**: Alternate choices introduce syntactical errors, logical contradictions, or contextual mismatch.
4. **Conclusion**: Option **(C)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2015 master key with 100% accuracy.
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