HOW TO solve N=4A+1;N=4 B+A+2;N=4C+A+B+3;N=4D+A+B+C+4;N=4 E+A+B+C+D+4
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How do you find the number of integral solutions of the equation 2x + 3y = 763?
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8 Answers
Manish Dodrajka, Digital Marketeer
Answered Apr 25, 2014
2x + 3y = 763
=> y = (763 - 2x)/3
It has infinite integral solutions as there are infinite integral values of 'x' for which 'y' is an integer.
But the equation has finite number of positive integral solutions and I have solved for it.
Now, for 'y' to be an integer, (763-2x) must be a multiple of 3.
A little observation tells us that it happens when
763-2x=759,753,747,741,735,729......15,9 and 3.
=> x=2,5,8,11,14,17.........371,374,377,380
For each value of 'x', y can be calculated.
The values of 'x' forms an A.P.
so,
380 = 2 + (n-1)3
=>n=127.
Hence, there are 127 solutions to the ...
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