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I don't know how to get started with this question. $11 = 4(x) + 5(y)$

What I've tried is :

$x = 0, y = 2$

$11 = 4(0) + 5(2)$

$11 = 10$

$11$ is not equal to $10$.

Wouldn't that be my base case? What more could I do to solve this question?

If i needed to apply induction to this question, how would I do it?

Any help is greatly appreciated.

Community
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MathNoob
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    If $x$ and $y$ can only be non-negative, then $x \leq 3$ and $y \le 2$ and you can just enumerate all possibilities. Otherwise, $x = -1$ and $y = 3$ is a solution – MBW Feb 15 '19 at 01:58

1 Answers1

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If you allow $x,y$ to be integers, then the claim is false: $11 = 4 \cdot (-1) + 5 \cdot 3$. If $x,y$ need to be non-negative, there are only $6$ cases to check. So you just do that manually.

Stefan Mesken
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