Solve the simultaneous equation: 2x + y = 18, x - y = 6

First, we simply label the two equations as 'Equation 1' and 'Equation 2' respectively. So we have: Equation 1: 2x + y = 18and Equation 2: x - y = 6. In simultaneous equations, there are two variables: x and y. We want to express one variable in terms of the other (x in terms of y or vice versa). There are many ways to do this but it is a good idea to choose one that is easiest for you. We can express x in terms of y by rearranging Equation 2. We add y to both sides of the equation which gives us: Equation 3: x = y + 6. We can now sub this into Equation 1 in order to find out what the value of y is. We know x = y + 6 so we sub in this equation into 2x. Therefore, Equation 1 becomes 2(y+6) + y = 18. When we expand the brackets out, we get 2y + 12 + y = 18. If we collect like terms, we can rewrite this as 3y = 6. To find the value of y, we simply divide both sides by 3 to get y = 2. We have solved one half of our simultaneous equation. We have found what y is but we now need to find x. This is easy if we use our Equation 3: x = y + 6. We simply sub in our value of y into Equation 3 which will give us: x = 2 + 6. Therefore we have found that x = 8. Thus our final solution can just be written as: x = 8, y = 2. We can check and double check our answers by subbing in these values into Equation 1 and 2 to see if they are true. If not, we have made a mistake. However, if they do work then we know we have definitely got the correct answer!