| Assertion (A): The lines \[\text{2x}-\text{5y}=\text{7}\]and \[\text{6x}-\text{15y}=\text{8}\] are parallel lines. |
| Reason (R): The system of linear equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]have infinitely many solutions if \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\]. |
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: B
Solution :
| [b] Two tines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] |
| and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] |
| are parallel if \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] |
| So, both assertion and reason are correct but reason does not explain assertion. |
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