
System of Inequalities
Both t and k are positive integers. What is the value of t? Multiple choice: 1, 2, 3, 4, or 5

I'm confused by the way this is worded... It seems to say that there is only one value of t which satisfies this system. But if I graph this, I get an entire region, not just one value? In fact, it would seem if I graph this I get no overlap of shaded regions. I don't get it.
I guess one way is to just start trying numbers, but there must be a better way?

t can't be 1 or 2 by the 2nd and 3rd inequality. Also, k > 4t which tell us t can't be 4 so t is 1, 2, or 3 but we know t isn't 1 or 2.

Quote:
Originally Posted by
Reiner
[1] (t + k)(t  k) < 6 [1A]
[2] t + k = 5 minimum [2A]
Substitute [2A] in [1A]:
5(t  k) < 6
So t  k < 2
[3] t > k
So t = 3, k = 2