Solve the following simultaneous equations: (1) 2y + x = 8, (2) 1 + y = 2x

The first aim is to obtain an expression for one of the unknowns in terms of the other. To achieve this, addition and subtraction methods are used. For example, using equation 1, subtracting 2y from both sides, gives x = 8 - 2y. This new expression is then substituted into the other equation (equation 2). This gives 1 + y = 2(8 - 2y), which when expanded gives 1 + y = 16 - 4y.Rearranging, again using addition and subtraction, gives 5y = 15. Dividing both sides by 5 gives y = 3. The next aim is to find the remaining unknown, x. This is done by substituting our known value of y into any of the original equations. E.g Using equation 2. 1 + 3 = 2x. Therefore giving 2x = 4, so x = 2. So we now have both of our unknowns. Just to be safe we could check our answer by back-substituting the answers into one of the equations. E.g. Using equation 1. 2(3) + 2 = 8, which is correct.