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

If \[{{2}^{x+y}}={{2}^{x-y}}=\sqrt{8},\] then the value of x and y are:

A) \[\frac{3}{2},0\]

B) \[0,\frac{3}{2}\]

C) \[\frac{2}{3},-1\]

D) \[1,\frac{2}{3}\]

Correct Answer: A

Solution :

[a] Given, \[{{2}^{x+y}}={{2}^{x-y}}=\sqrt{8}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,{{2}^{x+y}}={{2}^{x-y}}={{(8)}^{1/2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,{{2}^{x+y}}={{2}^{x-y}}={{2}^{3/2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,x+y=\frac{3}{2}\] and \[x-y=\frac{3}{2}\]

Adding both equations, we get

\[2x=3\Rightarrow x=\frac{3}{2}\]

and \[y=\frac{3}{2}-\frac{3}{2}=0\]