| Assertion (A): The system of equations are inconsistent: |
| \[\text{2x}+\text{4y}=\text{1}0\] \[\text{3x}+\text{6y}=\text{12}\] |
| Reason (R): A pair of linear equations which has no solution is called an inconsistent pair of Linear equations. |
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] The given system of equations can be written as |
| \[2x+4y-10=0,\] |
| \[3x+6y-12=0\] |
| Here, \[{{a}_{1}}=2,\,\,{{b}_{1}}=4,\,\,{{c}_{1}}=-10\] |
| \[{{a}_{2}}=3,\,\,{{b}_{2}}=6,\,\,{{c}_{2}}=-12\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{2}{3},\] |
| \[\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{4}{6}=\frac{2}{3},\] |
| \[\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{-10}{-12}=\frac{5}{6}\] |
| Clearly, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] |
| So, the given system of equations has no solution, i.e., it is inconsistent. |
| \[\therefore \] Assertion: True; Reason: True and it is the correct explanation of assertion. |
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