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Question

Consider the equation 2x+5y=13, where x,yϵN. Find the number of solutions of the equation.

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Solution

Given equation is 2x+5y=13
or 6y+15x=xy
or (x6)(y15)=90=2×32×5
Consider (x6) and (y15) as boxes.
Number of solutions is same as number of ways 2, 3, 3, 5 can be distributed in these boxes.
Number of ways 2 can be distributed =2
Number of ways 5 can be distributed =2
Number of ways (3, 3) can be distributed =3
Total number of solutions =2×2×3=12

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