Solve the simultaneous equations: 3x + y = 15 and 4y + 3 = 9x

The best way to solve simultaneous equations is by substitution. The first step is to pick a variable to eliminate. In this case, I'm going to choose to eliminate y because the first equation has a y on it's own with no number which means we can make y the subject without having to do any dividing or anything. Note that we could choose either variable from either equation and eliminate that, I'm just choosing the single y in the first equation because it will make the algebra easier as we will now see. Re-arranging the first equation for y gives y = 15 - 3x. We now have an expression for y. We substitute this expression into the other equation to attain one equation in terms of x. In the second equation we have 4y + 3 = 9x. However, instead of y, we're going to say 15 - 3x and the equation will still hold because y = 15 - 3x (y and 15-3x are the same!). We now have 4(15 - 3x) + 3 = 9x. We now want to solve for x. Expanding the brackets gives: 60 - 12x + 3 = 9x; collecting the 60 and the 3 gives: 63 - 12x = 9x; adding 12x to both sides gives: 63 = 21x; finally, dividing by 21 (to get x on its own) gives: x = 3. Woohoo! We're nearly done as we've got a value of x, all we need now is a corresponding value of y! We know from earlier that y = 15 - 3x. Substituting our x = 3 into this equation gives y = 15 - 3(3) = 15 - 9 = 6. Therefore: x = 3 and y = 6. We're done.