question_answer

The solution set of the following linear in equations \[x-2y\ge 0;\,\,\,2x-y\le -2;\,\,x\ge 0,y\ge 0\]is given by

A)  \[[1,\,\,2]\]              

B)  Null set

C)  \[x\ge 1\]               

D)  Set of real numbers

Correct Answer: B

Solution :

Given,  linear in equations are \[x-2y\ge 0;\,\,\,\,\,\,\,2x-y\le -2;\] \[x\ge 0,\,\,\,\,y\ge 0\] Since, the intersection point of both lines intersect in third quadrant, i.e., x and y coordinate are both negative but given that x and y are both positive. So, solution of given inequalities is ??Null set??.