Question

Draw the graph of the solution set of the inequations: 2x+y ≤ 2, x-y ≤ 1, x+2y≤8, x≥0 and y≥0​

Answer 1

Answer:

The solution set of the system of inequations is the set of all possible coordinates (x,y) that satisfy all of the inequalities. To graph the solution set, we can begin by finding the ordered pair that satisfy each inequality.

For 2x+y ≤ 2, we can graph the line 2x+y = 2 and shade the half-plane below it.

For x-y ≤ 1, we can graph the line x-y = 1 and shade the half-plane below it.

For x+2y≤8, we can graph the line x+2y = 8 and shade the half-plane below it.

For x≥0 and y≥0, we can graph the line x=0 and y=0 and shade the half-plane below it.

The intersection of these four half-planes is the solution set of the system of inequalities. The graph of the solution set is a polygon with four vertices (0,0), (2,0), (1,1), (4,2) and the solution set is all the points within that polygon and on the edges of it.

It's worth noting that this can be a bit difficult to graph this on paper, and it's more common to use software such as a graphing calculator or a computer program to graph the solution set.