If x and y can take only natural number values, find the number of (x,y) pairs satisfying the equation 2X + 5y = 100.

Answer 1

First, rearrange the equation to solve for y:

5y = 100 - 2x

y = (100 - 2x) / 5

For y to be a natural number, the numerator of the fraction has to be divisible by 5. Since 100 is divisible by 5, the numerator will also be divisible by 5 if 2x is divisible by 5.

This means x must be a multiple of 5.

Given that x is a natural number, the possible values for x are 5, 10, 15, ..., 45, 50. There are 10 possible values for x.

For each of these values of x we can substitute into the equation to find the corresponding value of y. For example, when x = 5: y = (100 - 2*5) / 5 = 90 / 5 = 18.

So, we have 10 pairs of (x, y) satisfying the equation:

(5, 18), (10, 16), (15, 14), (20, 12), (25, 10), (30, 8), (35, 6), (40, 4), (45, 2), (50, 0)

Answer 2

Above question only 9pairs satisfied .(50,0)is not a pair 0 is not a natural number.

Answer 3

You are correct. I apologize for the mistake.

The correct number of (x, y) pairs satisfying the equation 2x + 5y = 100 where x and y are natural numbers is indeed 9 pairs:

(5, 18), (10, 16), (15, 14), (20, 12), (25, 10), (30, 8), (35, 6), (40, 4), (45, 2)