A) a unique solution
B) exactly two solutions
C) infinitely many solutions
D) no solution
Correct Answer: A
Solution :
| [a] The given pair of equations is |
| \[2x-3y+4=0\]and \[2x+y-6=0\] |
| Here, \[{{a}_{1}}=2,\,{{b}_{1}}=-3,\,{{c}_{1}}=4,\,{{a}_{2}}=2,\,{{b}_{2}}=1,\,{{c}_{2}}=-6\] |
| Now, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{2}{2}=1,\,\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{-3}{1}=-3,\,\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{4}{-6}=\frac{-2}{3}\] |
| Since, \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\] |
| \[\therefore \] The given equations has a unique solution. |
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