Solve the following simultaneous equations for x and y : 2x - y = 12; x + 3y = 20

When solving equations such as these we have two variables which represent two numbers. In order to solve them we want to isolate and remove one of the variables so we are only left with one, we do this by moving one of the variables onto the other side of each equation. If we add 'y' to both sides of the first equation we end up with Equation A: 2x = 12 + y. If we then subtract '3y' to both sides of the second equation we arrive at Equation B: x = 20 - 3y.
We are nearly able to remove the variable 'x' but first we need to make sure that the number in front of the 'x' is the same. We could either divide the first equation by 2 OR we could multiply the second equation by 2. The second option will be much easier so we will do that. After multiplying the second equation we arrive at Equation C: 2x = 40 - 6y.
Now we can remove 'x' by subtracting Equation A from Equation C. The resulting equation is: 28 - 7y = 0. By rearranging and dividing the equation by 7 we find that y = 4. The last thing to do is to put the value of 'y' into the original two equations to work out the value of 'x'. The final answer therefore is x = 8, y = 4.