How many integer solutions exists for the equation 11x + 15y = -1 such

We need to find all possible integer solutions (values less than 100) of the equation 11x + 15y = -1

To answer this we need to find one solution first which can be found either using hit and try or using other methodical method

Let/s try some hit and try,

11x + 15y = -1
x = 3 and y = -2, 11x + 15y = 11*3 +15*(-2) = 3 ≠ -1
[b]x = 4 and y = -3, 11x + 15y = 11*4 +15*(-3) = -1[/b]

i.e. (x, y) = (4, -3) is the first solution

RULE: To find the next solution, value of x differs by co-efficient of y and value of y differs by co-efficient of x
i.e. x will differ by 15 and y will differ by 11
i.e .Next solution will be x = 4+15 = 19 and y = -3-11 = -14
@ (x, y) = (19, -14), 11x + 15y = 11*19 +15*(-14) = 209-210 = -1

i.e. solutions can be listed down as per rule as follows

(x, y) = (-131, 96)
(x, y) = (-116, 85)
(x, y) = (-101, 74)
(x, y) = (-86, 63)
(x, y) = (-71, 52)
(x, y) = (-56, 41)
(x, y) = (-41, 30)
(x, y) = (-26, 19)
(x, y) = (-11, 8)
(x, y) = (4, -3)
(x, y) = (19, -14)
(x, y) = (34, -25)
(x, y) = (49, -36)
(x, y) = (64, -47)
(x, y) = (79, -58)
(x, y) = (94, -69)

16 solutions

Answer: Option B