A) \[c=3\]
B) \[c=-3\]
C) \[c=-12\]
D) not possible for any value of c
Correct Answer: D
Solution :
| [d] The given pair of equations is |
| \[cx-y-3=0\] and \[6x-2y-4=0\] |
| For infinitely many solutions, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}.\] |
| Here, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{c}{6},\,\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{-1}{-2}=\frac{1}{2},\,\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{-3}{-4}=\frac{3}{4}.\] |
| So, \[\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] |
| So, there will be no value of c for which the pair of equations will have infinitely many solutions. |
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