Question:
The value of $\lambda$ and $\mu$ for which the system of equations
$x+y+z=6$, $x+2y+3z=10$ and $x+2y+\lambda z=\mu$ have no solution, are
The value of $\lambda$ and $\mu$ for which the system of equations
$x+y+z=6$, $x+2y+3z=10$ and $x+2y+\lambda z=\mu$ have no solution, are
Show Hint
Parallel equations with different constants → no solution.
Updated On: Apr 23, 2026
- $\lambda=3,\ \mu\ne 10$
- $\lambda\ne 3,\ \mu=10$
- $\lambda\ne 3,\ \mu\ne 10$
- None of these
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The Correct Option is A
Solution and Explanation
Concept:
System has no solution when equations are inconsistent.
Step 1: Compare equations.
\[ x+2y+3z=10 \] \[ x+2y+\lambda z=\mu \]
Step 2: Check proportionality.
For inconsistency: \[ \lambda = 3 \] but RHS differs.
Step 3: Condition for no solution.
\[ \mu \ne 10 \] Conclusion:
Answer = $\lambda=3,\ \mu\ne 10$
Step 1: Compare equations.
\[ x+2y+3z=10 \] \[ x+2y+\lambda z=\mu \]
Step 2: Check proportionality.
For inconsistency: \[ \lambda = 3 \] but RHS differs.
Step 3: Condition for no solution.
\[ \mu \ne 10 \] Conclusion:
Answer = $\lambda=3,\ \mu\ne 10$
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