| Assertion (A): The value of k for which the system of equations \[\text{kx}-y=\text{2},\]\[\text{6x}-\text{2y}=\text{3}\] has a unique solution in 3. |
| Reason (R): The system of linear equations\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]has a unique solutions if \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}.\] |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: D
Solution :
| [d] Given system of linear equations has a unique solution if |
| \[\frac{k}{6}\ne \frac{-1}{-2}\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\,\,\frac{k}{6}\ne \frac{1}{2}\] |
| \[k\ne 3\] |
| So. assertion is incorrect and reason is correct. |
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