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

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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?