Solve the simultaneous equations: a) 2x + y = 18, b) x - y = 6

Notice we have two different equations but that 'x' and 'y' take the same value in both equation a and equation b. In order how to work out what values they take we need to combine the two different equations to get one equation that encompasses all the information we have been give. We can see that by adding 'y' to both sides of equation b we will get 'x=6+y'. We now have a definition of 'x'. We can substitute this definition into equation a to work out the values of 'x' and 'y'. Therefore, we get '2(6+y) + y = 18', having replaced the 'x' with '6+y". By multiplying out this bracket we see that we get '12 + 2y + y = 18'. We can take 12 away from both sides and are left with '3y = 6'. Dividing both sides by 3, we are left with the fact that y = 2. Applying this information to the equation that 'x = 6 + y', we can now work out the value of 'x' too. Thus, 'x' is 6 + 2 = 8. We have worked out that x = 8 and y = 2.