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If |x|<100 and |y|<100, then the number of integer solutions of (x, y) satisfying the equation 4x + 7y = 3 is
Correct Answer: 29
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
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