You need to see through the problem and apply whatever is necessary to reduce the number of variables till eventually there's only one to find.
Remember a simple fact: if you have two variables you always need two independent equations to find them; for three variables, three equations; four variables, four equations.
You use the multiplication property if it helps you to eliminate a variable between two equations.
Take some examples: x+y=10, x-y=3; simply adding these two equations will eliminate y and help you find x.
2x=13 so x=6.5 and y=3.5;
2x+y=10, x-2y=10; we could double one equation or the other so as to match the coefficients of one or other of the variables; but since it's easier to add two equations rather than to subtract them, where we have a minus in one equation and a plus in the other, we would prefer to use the multiplier for the relevant variable.
So we double the first equation and add to the second: 4x+2y=20 PLUS x-2y=10: 5x=30, making x=6 and y=-2.
The last pair of equations could have been written: 2x+y=x-2y=10, but it's still two equations.
There is no one way to solve equations, and you can save yourself a lot of stress by not assuming you have to remember a rigid technique or formula as “The Way to do it”. You'll find mathematics is more fun when you intelligently try different methods and use your natural creativity to guide you.
And here's another interesting thing. Those questions about finding a missing number in a series can be tackled in many cases as solving simultaneous equations. You only need n equations to find n variables, and a series can be seen as a set of terms generated by a function y=f(x) for different values of x (the position in the series), giving different values of y (the terms in the series). f(x) is a polynomial of the type ax^n+bx^(n-1)+cx^(n-2)+... If there are four given terms n=3 and the variables are a, b, c and d; if there are 3 given terms, n=2 and the variables are a, b and c. There is always a solution, we just have to work through and find it! Read More: ...