Question

How many natural numbers satisfy the equation 34x+51y=126​

Answer 1

Answer:

380 = 2 + (n-1)3

=>n=127.

Step-by-step explanation:

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Answer 2

Given:

Consider the given equation 34x + 51 y = 126

Find:

Number of natural numbers that satisfy the equation

Solution:

Solving for y we have

51 y = 126 - 34x

y =$\frac{126-34x}{51}$

Since there are infinite number of integral values of x which satisfy this equation but we are intrested in positive integers that is natural numbers

make some observations

For y to be an integer the factor (126 - 34x) must be multiple of 51

And here the positive values of x for this condition is possible 1, 2, and 3

For 1

y =$\frac{126-34x}{51}$= 92/51 not an integer

similarly for x = 2 and 3 also we get rational not positive integer

Therefore there doesn't exist any positive interger that satisfy the given equation.