A) infinite number of solutions
B) unique solution
C) no solution
D) cannot say anything
Correct Answer: B
Solution :
Let \[\Delta =\left| \begin{matrix} {{a}_{1}} & {{a}_{2}} \\ {{a}_{4}} & {{a}_{5}} \\ \end{matrix} \right|\] \[={{a}_{1}}{{a}_{5}}-{{a}_{2}}{{a}_{4}}\] \[={{a}_{1}}({{a}_{1}}+4d)-({{a}_{1}}+d)\,({{a}_{1}}+3d)\] \[=a_{1}^{2}+4{{a}_{1}}d-a_{1}^{2}-4{{a}_{1}}d-3{{d}^{2}}\] \[=-3{{d}^{2}}\ne 0\] Hence, given system of equations has unique solution.
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