graph the system of inequalities x-2y>=6 and 2x+y<=6

Question

i really dont know where to start with this problem.

Answer 1

Given first inequlity x-2y ≥ 6

Convert the equations in to y = mx+b form

x-2y = 6

-2y = 6-x

y = -3+x/2

y = x/2-3

Second inequlity 2x+y ≤ 6

2x+y = 6

y = -2x+6

Now graph the two lines y = x/2-3 and y = -2x+6.

The graph of y = x/2-3 is included in the graph of the solution.

The graph of y = -2x+6 is included in the graph of the solution.

The boundary line of graph of y = x/2-3 is shaded with purple colour and the boundary line of graph of y = -2x+6 is shaded with meroon colour.

The soution of the system is the set of orderd pairs in the intersection of the graph of y = x/2-3 and y = -2x+6.

The region is shaded light purple colour.

Graph