I am getting stuck on how to solve Simultaneous Equations, can you explain how to do this?

I always find with simultaneous equations that it is first important to remember what you are actually trying to do- to work out the values of x and y given what you know about them. So lets use this example: 3x + 2y = 7 and 2x + y =4 . We know that as they are simultaneous equations then our values of x and y are the same. However, in its current form it is much too difficult for us to solve so we need to simplify it. To do this we want to be able to write an equation in terms of just one of x or y. The simplest way to do this is to rewrite them in a form where we can cancel out either the x or the y terms. Using our example it appears that the easiest way to do this is to multiply our second equation by 2 to make the y terms equal (Note- When multiplying an equation by a number you must do this to all parts of the equation). 3x + 2y =7 [Keep the same], 4x + 2y= 8 [ (2x + y = 4) x 2]. Now as you can see our y terms are equal which means that we should now subtract one equation from the other. As a general rule, I find that it is easier to subtract the equation with the smallest answer from the biggest one. 4x + 2y = 8 MINUS 3x + 2y = 7 EQUALS 1x + 0y = 1 therefore x = 1. Now we have established what x is all we need to do is plug it back into one of the initial equations to work out what y is. So: 2x + y = 4 becomes 2 + y = 4 so y = 2 Which means our answer is that x= 1 and y= 2!! An easy way to check it is to plug our answers back into the other equation and see if it works: 3x + 2y =7 becomes 3(1) + 2(2) = 7 which means that 7 = 7 so we have solved it :)