Draw the graph of the solution set of the inequation 2x + y ge 2, x-y le 1, x+ 2y le 8, x ge 0 and y ge 0

Draw the graph of the solution set of the inequation 2x + y ge 2, x-y

1.	Draw the graph of the solution set of the inequation 2x + y ge 2, x-y le 1, x+ 2y le 8, x ge 0 and y ge 0
Answer» Solution : First, we draw the graph of `2x + y ge 2` CONSIDER the line, 2x + y = 2. Now ` 2x + y =2 rArr x/1+ y /2 =1` This line meets the axes at A(l, 0) and B(O, 2). Clearly, the line AB represents 2x + y = 2. Now (0,0) does not satisfy` 2x+ y ge 2 ` Thus, the line AB and part of the plane separated by AB and not containing 0(0, 0), represent the solution set of `2x + y ge 2 ` (ii)Next we draw the graph of `x - y le 1` Consider the line, x-y = 1. `x-y = 1 rArr x/1 + y/((-1))=1` This line meets at the axes at A(1, 0) and C(0, -1). Clearly, the line AC represents x-y = 1. ALSO (0,0) SATISFIES `x - y le 1` Thus the line AC and part of the plane separated by AC and part of the plane separated by AC and containing O(0,0) represent the solution set of `x-y le 1 ` (iii) Now, we draw the graph of `x + 2y le 8` Consider the line, x + 2y = 8. Now `x+2y =8 rArr x/8+y/4=1` This line meets the axes at D(8, 0) and E(0, 4). So, the line DE represents x + 2y = 8. Also, (0, 0) satisfies the inequation, ` x+ 2yle 8` Thus the line DE and part of the plane containing O(0,0) represent the solution set of `x+2 le 8`. (iv) `x ge 0 ` is represented by the y-axies and the plane on its right (v) ` y ge 0 ` is represented by the x-axies and the plane above the x- axis. The intersection of all these planes is the REQUIRED shaded part , representing the solution of the gives system .