Anyway, if you want to do it by hand, it's just like with two variables. Solve an equation for one variable in terms of the others. You can do this a couple times and get two equations with two unknowns. Solve them normally then use that to find the 3rd solution.
Do you mean the following?:
4 = a + b + c .... (1)
10 = 4a + 2b + c .... (2)
18 = 9a + 3b + c .... (3)
The following will give you two equation in a and b:
Equation (2) - equation (1):
Equation (3) - equation (1):
Solve them for a and b. Then use those values in one of the equations to solve for c.