A) a unique solution
B) no solution
C) infinitely many solutions
D) None of these
Correct Answer: B
Solution :
| [b] Given, \[2x-2y-2=0\] and \[4x-4y-5=0\] |
| Here, \[{{a}_{1}}=2,\,\,{{b}_{1}}=-2,\,\,{{c}_{1}}=-2\] |
| and \[{{a}_{2}}=4,\,\,{{b}_{2}}=-4,\,\,{{c}_{2}}=-5\] |
| \[\therefore \,\,\,\,\,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{2}{4}=\frac{1}{2},\,\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{-2}{-4}=\frac{1}{2}\]and \[\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{-2}{-5}=\frac{2}{5}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] |
| which shows that the given equations' have no solution. |
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