I'm not sure how to do this....

Question

Which of the following points is within the solution region?

(-5, 4); (2, 5); (-5, -2)

  

Answer 1

plot each point

if the point is in the shaded region it is a solution

if the point is not in the shaded region or if the point is on the dotted line it is not a solution

Answer 2

Hi Lucy S.,

Nice diagram.

So, it shows two inequalities, right, each one is partially shaded blue, and the intersection region (darker blue) is the region that satisfies BOTH inequalities. So mentally, or physically, place those three specified points onto that Cartesian coordinate plane, and see if they are in the dark blue region, or not! (If they are, they are in the "solution region", or whatever else you may want to designate it as.)

When faced with such a problem, always assume that the shading, hatching, etc. is some sort of target region, and that the unshaded, etc. portion is not part of the target region. That would only be reasonable, unless you have like 50 inequalities superposed, and it would make more sense to look for a white region than try to sort through 50 shades for the darkest blue! But if that were to be the case, the problem description, etc. would make that explicitly clear. I hope!

-- Cheers, -- Mr. d.

P.S. I say, "I hope", because I'm color blind, and occasionally map makers lovingly color maps up with 30 shades, and it's impossible for me to match subtle gradations on the map key to those on the actual map, some visual distance away across many boundaries .... b/c of the boundaries, and also b/c display screens don't display colors the same in all directions, so that the colors are really different anyway by the time you glance from one place to the other .... Moral: if you present such complex maps, use multiple visual cues on the shadings = luminosity + chroma + hatching + other_cues, etc.; mix these cues up in the series, so that they will make each "shading" very distinct from its immediate neighbors!