Question

Write all the possible solutions of the form (a,0), a∈N for 3x+4y≤15

Answer 1

3x+4y≤15
we have to write solution in the form of (a,0) and a∈N
so, y=0
so,
3x≤15
we have to find only natural numbers satisfying 'x',
so
put,
x=1 then....value is 3........satisfied
x=2 then..value is 6.........satisfied
x=3 then..value is 9.........satisfied
x=4 then..value is 12.........satisfied
x=5 then..value is15.........satisfied

x=6 then..value is 18.........not satisfied
this inequalityis not satisfied for any natural number value greater than 5.
so answer is...
(1,0),(2,0),(3,0),(4,0),(5,0)

Answer 2

3x+4y≤15
given solutions must be in form of (a,0),so y=0
that is 3x≤15
           x≤5
   so (1,0),(2,0),(3,0),(4,0) and (5,0) are solutions