I need help understanding simultaneous equations with more than two variables, can you please help?

Working with more than 2 variables in simultaneous equations can be daunting at first, but as long as you apply the same methods you have learned for simpler problems, you will get used to these more complex questions. As long as you have the same number of variables and unique equations, you will be able to solve them. Let's look at an example question:
Solve the simultaneous equations below for a, b and c:4a + b + 3c = 14 (i)2a - 2b + c = 12 (ii)2a + 3b - c = -13 (iii)
And the example solution is as follows:Sum (ii) and (iii) to remove c: 4a + b = -1 (iv)Sum (i) and 3 x (iii) to remove c: 10a + 10b = -25 (v)We now have 2 equations for x and y so we can solve these two variables.Take (v) from 10 x (iv): 30a = 15Divide both sides by 15: 2a = 1Divide both sides by 2: a = 0.5Put a into (iv): 4 x 0.5 + b = -1 => 2 + b = 1Take 2 from both sides: b = -3Put a and b into (i): 4 x 0.5 + (-3) + 3c = 14 => -1 + 3c = 14Add 1 to both sides: 3c = 15Divide both sides by 3: c = 5If you want to check, try putting a, b and c into one of the other equations: 2 x 0.5 - 2 x (-3) +5 = 1 - (-6) + 5 = 12 which is correct.Therefore: a = 0.5 , b = -3 , c = 5