how to solve these equations

50 + a - c = 75...(1)
c + b - 25 = 50...(2)
a + b = 100...(3)

From (2) and (3): a = 100 - b, c = 75 - b

Sub. into (1) 50 + 100 - b - 75 + b =75 => 0 = 0

This means that (1) can be derived by (2) and (3)

So, the solution is (a,b,c) = (100 - t, t, 75 - t) where t is a real number.

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The method of solving this kind of question is eliminating the variables until one is remained by combining the equations

50 + a - c = 75
a - c = 25 .... [1]

c + b - 25 = 50
b + c = 75 .... [2]

a + b = 100 .... [3]

It is observed that there is -c and c in equation [1] and [2] respectively.
By adding [1] and [2], we obtain:

(a - c) + (b + c) = 25 + 75
a + b = 100

It is same as equation [3].
Therefore, the answer of this question is "many solutions".