| Assertion (A): Pair of linear equations: \[9x+3y+12=0,\] \[\text{8x}+\text{6y}+\text{24}=0\] have infinitely many solutions. |
| Reason (R): Pair 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: A
Solution :
| [a] From the given equations, we have |
| \[\frac{9}{18}=\frac{3}{6}=\frac{12}{24}\] |
| \[\frac{1}{2}=\frac{1}{2}=\frac{1}{2}\] |
| i.e, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] |
| So, both assertion and reason are correct and reason (R) explains assertion. |
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