Question 126
How many integer solutions exists for the equation 11x + 15y = -1 such that both x and y are less than 100 ?
Solution
11x + 15y = -1
Solution of this equation will be of the form x=a+15k , y=b-11k, where (a,b) is any solution of the equation
We can clearly see that x=4,y=-3 is one solution of the equation.
x=4+15k, y=-3-11k
Given x<100,y<100
4+15k<100, k$$\le\ $$6 and -3-11k<100, k$$\ge-9\ $$
$$-9\le\ k\ \le\ 6$$, k can take 16 values.
There exists 16 solutions for the equation.
Option D is the answer.
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