Question

If (2s + 1, –s) is a solution of the equation 6x – 9y = 30, then find the value of 2s + 1.
fast tell

Answer 1

Step-by-step explanation:

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 equation.

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