Solve the simultaneous equations: 5x + y = 21 and x - 3y = 9

First, we must rearrange these equations to make them easier to work with. There are many ways to do this, but I will rearrange them so they both look like x=_____ so that we can temporarily eliminate x from the problem. When rearranging, the most important thing is to do the same thing to each side of the equation.So, starting with the first equation, take away y from each side to give 5x = 21 - y. Then divide both sides by 5 to give x = 21/5 - y/5, which looks like what I was aiming for. Now take the second equation and add 3y to each side to give x = 9 + 3y.Now we have two simultaneous equations x = 21/5 - y/5 and x = 9+3y which are equivalent to the two we started with but are easier to solve.Both equations have x on one side and clearly x=x so we can say 21/5 - y/5 = 9 + 3y. We must rearrange this to read as y=____. First multiply everything by 5 to get rid of the fractions, which gives 21 - y = 45 + 15y. Then add y to each side to give 21 = 45 + 16y. Then take away 45 from each side to give -24 = 16y. Now divide by 16 to give -24/16 = y. This simplifies to y = -3/2 which is the first part of the answer!Now we need to find x. We know x = 9 + 3y from earlier, so we substitute in the answer we just found for y, so we have x = 9 + 3(-3/2). Next, expand the brackets to give x = 9 - 9/2, which simplifies to x = 9/2. So we have solved the problem! Remember to clearly state the answers together at the end of the solution: x = 9/2 and y = -3/2.