Solving the Diophantine equation $7x+4y=100$

Question

I have attempted to solve this Diophantine equation:

But the solution I got is different from the one given above, my general solution is:

$x = -100 + 4t$ & $y = 200 - 7t$ , is the solution given above is correct or my solution is correct ? could anyone check this for me?

Note:

In my solution I have found the greatest common divisor of 4 and 7, which is 1 and then I have written it as a linear combination of 7 and 4, then I have multiplied the resulting equation by 1.

This is from the book of David M. Burton "elementary number theory", seventh edition, pg.37

Answer 1

Both are correct, is just different parametrizations of the same thing. Your solution is $x=-100+4t=4(t-25)$, $y=200-7t=25-7(t-25)$