Question

What is the system of equations that describes the following graph?

Answer 1

well, for one we can deduce it has no y component, and the other has a linear equation.

Answer 2

Well, there appears to be an \(x \ge 3\) in there. What's the other one?

Answer 3

–x + y < 1
x > 3

–x + y ≤ 1
x ≥ 3

–x + y ≥1
x ≥ 3

–x + y ≤ 1
x ≤ 3

those are my options

Answer 4

@tkhunny how do i figure out the rest?

Answer 5

I NEVER look at the answers. I get it right, first.

We've already ruled out the 1st and the 4th.

Notice how ALL the others are "-x + y something 1"

It's a solid line, so the 1st is out again!

Sometimes, the easiest way to do it quickly is to try something simple. (0,0) is often the easiest. Notice how (0,0) is NOT in the shaded region. Test out the remaining candidates and see which ones do NOT include the Origin.

Answer 6

neither of the remaining ones are in the shaded region...

Answer 7

Come on! Be more careful. (0,0) is NOT in the desired region. If you get "No, No", you should have it.

Is (0,0) in this region?
–x + y < 1 Yes
x > 3 No

–x + y ≤ 1 Yes
x ≥ 3 No

–x + y ≥1 No
x ≥ 3 No

–x + y ≤ 1 Yes
x ≤ 3 Yes

This should be quick. Substituting zero should not challenge you. Organizing your thoughts is the hard part. Why does this work?