How do you solve simultaneous equations

So let's use 2x + 5y = 11 and 3x - 5y = 4 as our example.In these equations we have 2 unknown variables, x and y which we are trying to work out. The numbers in-front of the letters are the amount of times we multiply the letter. For example 2x means 2 times by x and 5y means 5 times by y.So first thing to do is to line up the equations so that the same terms are underneath one another like this:2x + 5y = 113x - 5y = 4Now to start this problem we want to eliminate (get rid of) one of the letters. In this example we would get rid of the y as they are both times by 5 so it makes it easier. So how do we get rid of the y? Well to get rid of a letter we either have to add the 2 together or subtract them. As we have +5y and -5y, if we add these together they will make 0, therefore cancelling them out. Now we know we are adding the 2 equations we can lay it out like this:2x + 5y = 11+ 3x - 5y = 4----------------------------------------------So we now take each term and add them together. 2x + 3x = 5x. 5y + -5y = 0. 11 + 4 = 15.So the equation now looks like this:2x + 5y = 11+ 3x - 5y = 4---------------------5x + 0y = 15 which can be simply put as 5x = 15.---------------------So to get what x by itself, we want to move the 5 in-front of the x to the other side. On the left hand side we see it written as 5x which we know means 5 times by x so to move it onto the other side we do the opposite which is divide by 5. Remember what we do to one side we have to do to the other so we have to divide 15 by 5 which is 3. Therefore x = 3.Next you can substitute x = 3 into one of the equations, lets try equation 2x + 5y = 11.So (2 x 3) + 5y = 11 which simplifies to 6 + 5y = 11.Now we want all the letters on one side and all the numbers on the opposite. So we have to move the 6 over to the other side. On the left hand side it is +6 so to move it onto the other we -6 and remember you do it to both sides.5y = 11 - 65y = 5Then to get y by itself we have to divided by 5 (like what we did for x above).y = 5/5y = 1The answer is x = 3 and y = 1.If you want to check your answers you can then substitute your answers for x and y into the original equations and see if you get the correct answer.