If |x|<100 and |y|<100, then the number of integer solutions of (x, y) satisfying the equation 4x + 7y = 3 is

Given |x|<100 and |y|<100

or, -100<x<100 and -100<y<100

Now, 4x + 7y = 3

The orderd pairs satisfying this equation will be: (-1,1),(6,-3),.....

The values of x will be in an A.P. with common difference 7

Since x=-1 is a possible value,

Let's write the general term for other values of x as $$-1+\left(n-1\right)\cdot7$$

Now, x<100, so the maximum value of n can be 15, for which x=97

Also, -100<x, so the minimum possible of n can be -13, for which x=-99

So, basically values of n are from -13 to 15, that is 29 values

For each 29 values of n, we will get 29 values of x or 29 ordered pairs satisfying the equation and the constraint given.

So, number of integer solutions = 29