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

To solve these simultaneous equations there are two different methods that could be used. The first one to try in this case is to start with rearranging one of the equations to get a value of y by itself. For example, rearranging the second equation by adding y to both sides, which gives x-y+y=6+y which then gives x=6+y, then taking away 6 from both sides, giving x-6=y. This formula can then be subbed into the first formula, changing the y for what it is equal to, the x-6. Resulting in this equation 2x+x-6=18, leaving an equation with only one variable, the x. Then solving, we add the x terms together, and add 6 to both sides, giving 3x=24, then diving by 3 on both sides gives that x=8. This then leaves one final step, to find the y value we then sub x=8 into the y=x-6 equation, giving that y=8-6=2. Hence the solution to these simultaneous equations are x=8, y=2.Another method that can be used is lining up the equations one under the other like so,2x+y=18x-y=6And because there is +1y in the top equation and -1y in the bottom equation, if we then add both of these equations together, the resulting equations leaves us with no y values so we are left with an equation with one variable so we can work out the x value;3x+0y=24, and hence dividing both sides by three we are left with x=8, and subbing the x value into original equation leaves us with y=2 again, as desired.