A) \[\alpha =3,\,\,\beta =8\]
B) \[\alpha =4,\,\,\beta =8\]
C) \[\alpha =8,\,\,\beta =4\]
D) \[\alpha =1,\,\,\beta =2\]
Correct Answer: B
Solution :
The given system of equation will have infinite number of solutions if\[\frac{a}{2\alpha }=\frac{3}{\alpha +\beta }=\frac{7}{28}\] \[\Rightarrow \] \[\frac{1}{\alpha }=\frac{3}{\alpha +\beta }=\frac{1}{4}\Rightarrow \frac{1}{\alpha }=\frac{1}{4}\] and \[\frac{3}{\alpha +\beta }=\frac{1}{4}\] \[\Rightarrow \] \[\alpha =4\]and\[\alpha +\beta =12\] \[\Rightarrow \] \[\alpha =4\]and\[\beta =8\]
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