Question

The system of equations \[ 2x + y - 5 = 0, \quad x - 2y + 1 = 0, \quad 2x - 14y - a = 0 \] is consistent. Then, \( a \) is equal to:

• A. 1
• B. 2
• C. 5
• D. None of these

Hint:

To solve a system of linear equations, use methods like substitution, elimination, or matrix determinant conditions for consistency.

Answer 1

The Correct Option is D

Step 1: Use the system of equations.
For the system to be consistent, the determinant of the coefficient matrix must be zero. Solving the system will give the value of \( a \).
Step 2: Conclusion.
Thus, \( a = 5 \).
Final Answer: \[ \boxed{5} \]