Question

11x+13y=1000 ,then possible values of x and y

Answer 1

11x + 13y = 1000 is a linear equation of two variables. there are lot of value of x and y in which equation is satisfied. because we have given just a equation.

if we assume x = 0,
11 × 0 + 13y = 1000 => y = 1000/13
so, (0, 1000/13) is a solution of given equation.

if we assume x = 1,
11 × 1 + 13y = 1000 => y = (1000 - 11)/13
y = 989/13 = $76\frac{1}{13}$
so, $\left(1,76\frac{1}{13}\right)$ is also a solution of given solution..

similarly, you can get many solutions , just assume value of x or y and then get solutions of equation.

Answer 2

13y = 1000 (mod 11)

2y = -1 (mod 11)

12y = -6 (mod 11)

y = 5 (mod 11)

Thus y = 11k + 5 for some integer k.

11x + 13(11k + 5) = 1000

11x + 143k + 65 = 1000

11x + 143k = 935

x + 13k = 85

x = 85 - 13k