A) \[3\]
B) \[-3\]
C) \[-12\]
D) no value
Correct Answer: D
Solution :
| [d] The given equations of lines are |
| \[cx-y=2\] and \[6x-2y=3\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,cx-y-2=0\]and \[6x-2y-3=0\] |
| Here, \[{{a}_{1}}=c,\,{{b}_{1}}=-1,\,\,{{c}_{1}}=-2\] |
| and \[{{a}_{2}}=6,\,\,{{b}_{2}}=-2,{{c}_{2}}=-3\] |
| Since, condition for infinitely many solutions is |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\Rightarrow \frac{c}{6}=\frac{-1}{-2}\] and \[\frac{c}{6}=\frac{-2}{-3}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,c=3\] and \[c=4\] |
| Since, c has different values. |
| So, there exists no value of c for which given equations have infinitely many solutions. |
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