10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

Given the pair of equations \[ax+(a-1)y=1\] and \[(a+1)x-ay=1,\] for which one of the following values of is there no common solution of the given pair of equations?

A) \[\pm \sqrt{2}\]

B) \[\pm \frac{1}{\sqrt{2}}\]

C) \[\pm 2\]

D) \[1\pm \frac{1}{2}\]

Correct Answer: B

Solution :

[b] \[\frac{a}{a+1}=\frac{a-1}{-a}\ne 1\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,-{{a}^{2}}={{a}^{2}}-1\,\Rightarrow \,\,2{{a}^{2}}=1\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,{{a}^{2}}=\frac{1}{2}\,\,\,\,\,\,\Rightarrow \,\,\,\,a=\pm \frac{1}{\sqrt{2}}\]