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:
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:
Show Hint
To solve a system of linear equations, use methods like substitution, elimination, or matrix determinant conditions for consistency.
Updated On: Jan 6, 2026
- 1
- 2
- 5
- None of these
Show Solution
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The Correct Option is D
Solution and Explanation
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: \[ \boxed{5} \]
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: \[ \boxed{5} \]
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