A) \[a=1,b\ne 9\]
B) \[a\ne -1,b=9\]
C) \[a=-1,b=9\]
D) \[a=-1,b\ne 9\]
Correct Answer: D
Solution :
If the system of equations has no solution then \[\Delta =0\] and at least one of \[{{\Delta }_{1}},{{\Delta }_{2}}\]and \[{{\Delta }_{3}}\] is not zero. \[\Delta =\left| \begin{matrix} 1 & a & 1 \\ 1 & 2 & 2 \\ 1 & 5 & 3 \\ \end{matrix} \right|=0\] \[\Rightarrow -a-1=0\Rightarrow a=-1\] \[{{\Delta }_{2}}=\left| \begin{matrix} 1 & 1 & 3 \\ 1 & 2 & 6 \\ 1 & 3 & b \\ \end{matrix} \right|\ne 0\] \[\Rightarrow b\ne 9\]
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