| Assertion (A): The system of equations \[\text{2x}+\text{3y}+\text{5}=0\] and \[\text{4x+ky}+\text{7}=0\] is inconsistent when \[\text{k}=\text{6}\]. |
| Reason (R): The system of equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] is inconsistent when \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\]. |
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: A
Solution :
| [a] For the given system to be inconsistent, we have |
| \[\frac{2}{4}=\frac{3}{k}\ne \frac{5}{7}\,\,\,\,\,\Rightarrow \,\,k=6\] |
| So, Assertion: True; Reason: True and it is the correct explanation of assertion. |
You need to login to perform this action.
You will be redirected in
3 sec
