find all possible roots of an equation of the form ax + by + cz = d

Question

let's take for example the equation 5x + 10y + 15z = 100. What values ​​should the variables x, y, z have for the equation to be true

Answer 1

what exactly are you trying to achieve here?
That single equation in three variables has solution-set of (x,y,z) such that they fall on a unique plane in 3D space.
Now, mind you, planes are infinite in stretch (length x breadth) constituted of infinite points and therefore our solution set would also be an infinite set of points (x,y,z)... which essentially means that even a supercomputer would take infinite time to compute it.

Answer 2

@Gordie, thx for the correction dear.

Answer 3

5x= 100-10y-15z
5x = 5(20-2y -3z)
x = 20 - 2y -2z

choose y,z as you want

Answer 4

3x = 100 -10y -15z

right side must be 3*a

in rekation to x%3
100 is modulo 1
15* z is modulo 0
10y is 9y + y
9y is modulo 0
y must be modulo 2

y= 2,5,8,....

Answer 5

3x = 100 -10y - 11z
....same as before...

related to 3

100 is modulo 1
10y = 9y + y
11z = 12z -z
-y+z must be modulo 2

Answer 6

ax = d + cy + dz

(d + cy + dz ) mod a = 0
d mod a + cy mod a + dz mod a= 0
d mod a = f
....

Answer 7

on sololearn one says thank you with an upvote
(-;

Answer 8

Thank you bro