If the system of inequalities `y le -x +1 and y lt 1/2x` is graphed on the above polane which of the quadrants contain (s) no solutions to the system?

Options

A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrants I and II

Answer

B

Explanation

Draw a sketch of the two lines to help vasualize the system of inequalities.

Clearly, quadrants III and IV contain solutions to the system. Eliminate (C ). Quadrant II contains no solutions, so you can also eliminate (A). Look closely at quadrant I.The line for `y le -x + 1` intersects both the x and y axes at +1. The line for `y lt 1/2z` passes through the origin and upward into quadrant I. Thus, there is a very small triangle of solutions to both inequalities that lies in quadrant I. Therefore , (B) is correct.