SOLUTION: Can you please explain what I'm supposed to do here? Choose a point within the boundaries of the shape, and show algebraically that the point satisfies all of the inequalities.

Algebra ->  Graphs -> SOLUTION: Can you please explain what I'm supposed to do here? Choose a point within the boundaries of the shape, and show algebraically that the point satisfies all of the inequalities.       Log On


   

Question 931719: Can you please explain what I'm supposed to do here?
Choose a point within the boundaries of the shape, and show algebraically that the point satisfies all of the inequalities.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Take your point and put it in each of the inequalities and verify that the inequality holds.
Example: 2x%2By%3C1 and x%5E2%2By%5E2%3C2 represent a circle cut by a line.
Check points (-1%2F2,1%2F2) (1,1) to see if they are in the solution region.
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First (-1%2F2,1%2F2)
2%28-1%2F2%29%2B%281%2F2%29%3C1
-1%2B1%2F2%3C1
-1%2F2%3C1
True
%28-1%2F2%29%5E2%2B%281%2F2%29%5E2%3C2
1%2F4%2B1%2F4%3C2
1%2F2%3C2
True
Both inequalities are satisfied, (-1%2F2,1%2F2) is in the solution region.
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Next, (1,1)
2%281%29%2B1%3C1
3%3C1
False.
Since it already failed one of the inequalities, it is not in the solution region.