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

With linear simultaneous equations the best thing to do is find one variable first and in this question we will find x first. We will start by rearranging the second equation to give us y = x - 6. Now we will substitute this into the equation above so there is only one unknown which is x. The first equation now becomes 2x + (x -6) = 18. If we open up the brackets we then have 2x + x - 6 = 18 which simplifies to 3x - 6 = 18. We then move the six to the other side which means we add 6 to the 18. The equation is then 3x = 24. We then divide both sides by three and so x= 8. Now that we’ve found x, finding y is the next step. We use the value of x in the second equation. So it’s now 8 - y = 6. So we want a positive y on one side so we move it to the other side to get 8 = 6 + y. Finally to find y we subtract 6 but from both sides so we get y =2. We’ve solved the simultaneous equation!