How do you solve simultaneous equations?

I will run through an example of how to solve a set of simultaneous equations. In simultaneous equations you are given two or more algebraic equations and you need to solve them for the variables, usually called x and y. You start off by trying to get equivalent coefficients for either the x or y value in both of the equations.  For example: (1) 4x + y = 24 and (2) 7x + 3y = 47. Here we can multiply equation (1) by 3 so that both the x coefficients are equal to 3. So 3*(1) is equivalent to 12x + 3y =72. Now we can subtract (2) from 3*(1). This gives 5x + 0y = 25, giving 5x = 25 therefore x = 5. Substituting x back into equation (1) we get 4*5 + y =24. So y = 24 - 20 and y = 4. Giving us the solutions: x=5 and y=4.