A) a unique solution
B) exactly two solutions
C) infinitely many solutions
D) no solution
Correct Answer: D
Solution :
| Given, equations are \[x+2y+5=0\] |
| and \[-3x-6y+1=0\] |
| Here, \[{{a}_{1}}=1,\,{{b}_{1}}=2,\,{{c}_{1}}=5\] |
| and \[{{a}_{2}}=-3,\,{{b}_{2}}=-6,\,{{c}_{2}}=1\] |
| \[\therefore \,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=-\frac{1}{3},\,\frac{{{b}_{1}}}{{{b}_{2}}}=-\frac{2}{6}=-\frac{1}{3},\,\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{5}{1}\] |
| \[\therefore \,\,\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] |
| Hence, the pair of equations has no solution. |
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