Posted by Austin on Tuesday, September 4, 2012 at 12:00pm.
how many solution sets? from zero to the degree of the equation.
do they have to satisfy both? Yes.
In what case might they not? They have to satisfy both, or it is not a solution.
by definition, a solution set must satisfy all of the inequalities. Otherwise, it's not a solution.
The number of solution sets depends on the particular problem. There may be none at all, as in
x+y > 6
x+y < 0
Or there may be an unbounded one, as in
x+y > 3
x-y > 2
or a bounded one, as in
x+y > 3
x-y > 2
3x+y < 10
a visit to wolframalpha.com will let you play around with some. For the last example, just type
solve x+y > 3, x-y > 2, 3x+y < 10
and it will show the solution sets and graph the region.
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