CBSE Class 12-science Answered
Dear Student,
I believe you are asking about the number of non-negative integral solutions of the given equation, otherwise there can be infinite number of solutions if we allow x and y to be negative.
Assuming that we seek for non-negative solutions, consider two cases :
Case 1: if y is even => y = 2k + 1 ( where k is some non-negative integer).
Putting y = 2k +1 in given eqn., we get
2x + 3(2k +1) = 2001
=> 2x + 6k = 2001 -3 = 1998
=> 2x = 1998 - 6k
=> x = 999 - 3k
It is evident that for all values of k ∈ {0,1,2,3,4,...,333}, x will be a non-negative integer.
Hence, the ordered pair (x,y) ≡ (999 - 3k , 2k +1) , where k ∈ {0,1,2,3,4,...,333}.
i.e., there are 334 such ordered pairs or non-negative integral solutions of the equation.
Therefore, option (b) is correct.
Regards,
Topperlearning.