A) a unique solution
B) exactly two solutions
C) infinitely many solutions
D) no solution
Correct Answer: D
Solution :
| [d] The given equations are \[x+3y+5=0\] and \[-3x-9y+2=0\]. |
| Here, \[{{a}_{1}}=1,\,\,{{b}_{1}}=3,\,\,{{c}_{1}}=5,\,\,{{a}_{2}}=-3,\,{{b}_{2}}=-9,\,{{c}_{2}}=2\] Now, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{-1}{3},\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{3}{-9}=\frac{-1}{3}\]and \[\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{5}{2}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] |
| \[\therefore \] The given pair of equations has no solution. |
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