Question

The solutions to the inequalities 0≤x≤2, 0≤y≤1, and y≤−1/ 2 x+3/ 2 form a polygonal region in the plane.? how many sides does this polygon have?

Answer 1

for inequality
`0 \leq x \leq 2`, draw the lines
`x=0` and
`x=2`

for inequality
`0 \leq y \leq 1`, draw the lines
`y=0` and
`y=1`

for inequality
`y \leq - (1)/(2)x+ (3)/(2)` plot the line on the graph

As shown in the diagram below, the region enclosed form a polygon of five sides (pentagon)