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the OA is B. But i honestly thought that this question was mean because we always understood that an equation with 2 variables can never be solvable, now i'm seeing the contrary here. is there any other way to solve this problem without manually coming up with different numbers to experiement with? i don't usually like coming up with numbers because it can waste time. are there any direct steps that one can take? when can we say that 2 variables with only 1 equation is solvable and when not???

I selected B and got it right on my practice exam, but I too was curious about the theoretics behind this. Is something considered solvable even if you have to simply try out every combination? Conversely, if there is only one solution, does it by definition mean there must be a mathematical way of solving it?

I found answer following this reasoning:
- we have 23*a + 21*b=130
- a and b are both integers (this is actually a second constraint)
In order to restrict the possiblities, we can look at the unit digits of 23 and 21 (3 and 1) and note that we need to have 3*a + 1*b= "number with 0 as unit digit"
Thus we have the folloiwing possiblities:
- a=3, b=1
- a=2, b=4
- a=1. b=9

The only one which gives the initial formula equal to 130 ia for a=2 and b=4.