How do a system of four equations with Python?

[magpie]

The need to find a solution to the system is to provide an example of such a combination of natural numbers r, b, y, p, to be followed by the following equation system.

(r + b + y) = 12
(r + b + p) = 16
(r + y + p) = 14
(y + b + p) = 24

We know this combination is one.

[rosemadder]

For example, almost in the forehead, but quicker:

for r in range(-100, 100):
    for b in range(-100, 100):
        y = 12 - r - b
        p = 16 - r - b
        if r + y + p == 14 and y + b + p == 24:
            print(b, p, r, y)

In fact, the task on paper is:

1. We're folding all equations and getting

    (r + b + y) + (r + b + p) + (r + y + p) + (y + b + p) = 12 + 16 + 14 + 24
    3r + 3b + 3p + 3y = 66
    r + b + p + y = 22
   

2. further deduct from the equation all equations and variables are obtained:

    (r + b + p + y) - (r + b + y) = 22 - 12
    p = 10
   (r + b + p + y) - (r + b + p) = 22 - 16
   
   y = 6
   (r + b + p + y) - (r + y + p) = 22 - 14
   
   b = 8
   (r + b + p + y) - (y + b + p) = 22 - 24
   
   r = -2