Question

How do you graph the system `x+y >=1` and `x+2y >1`?

Answer 1

Solve the system:
(1) `x + y - 1 >= 0`
(2) `x + 2y - 1 > 0`

Explanation:

First graph the Line (1): x + y - 1 = 0, by its intercepts:
Make x = 0 --> y = 1 and make y = 0 -> x = 1
Use number line and the origin O as test point. Substitute x = 0 and y = 0 into inequality (1), we get:`-1 >= 0.` It is not true, then the solution set is the area not containing O. Color or shade this area.
Next, graph the Line (2): x + 2y - 1 = 0, by its intercepts.
Make x = 0 -> y = y = 1/2. Make y = 0 -> x = 1.
Substitute x = 0 and y = 0 into inequality (2), we get: -1 > 0. Not true, then the area solution set doesn't contain O. Color it.
The combined solution set is the commonly shared area.