A) a unique solution
B) no solution
C) infinitely many solutions
D) None of these
Correct Answer: C
Solution :
| [c] Given, \[3x-5y=7\] and \[9x-15y=21\] |
| Here, \[{{a}_{1}}=3,\,\,{{b}_{1}}=-5,\,\,{{c}_{1}}=7\] |
| and \[{{a}_{2}}=9,\,\,{{b}_{2}}=-15,\,\,{{c}_{2}}=21\] |
| Now, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{3}{9}=\frac{1}{3},\,\,\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{-5}{-15}=\frac{1}{3}\] |
| and \[\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{7}{21}=\frac{1}{3}\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] |
| which shows that the given equations have infinitely many solutions. |
You need to login to perform this action.
You will be redirected in
3 sec
