The question:
How many integral solutions does the equation 2x+3y=8 have such that 100<x<200?
Solution:
Blockquote
× = 4-3/2y (after rearranging)
Hence,
If x = 4, y = 0
If × = 7, y = - 2
If x= 10, y = -4
As given above, for integral solutions, the value of x increases in steps of 3, with the first integral value above 100 being 103. Hence, there are 33 integral solutions for the given range of x.
Wondering if anyone has a simpler approach? This would never be where my mind initial goes.
