2x + 4 = 4y ; 3y + 3 = 3x. What is x and y respectively?

Firstly you need to identify the information in the question that is key. On analysing the question, you will see that the objective is to find what x is and what y is respectively. We are given two separate formulas that use a combination of x and y. On their own, we will not effectively be able to work out what x and y is from using one formula alone. However, by combining the two equations, we can get to the bottom of the equation! It is important to simplify the equation in one of two ways. We can either make x the subject or make y the subject. Once we have done this, we can substitute back into the other equation to work out one of the letters.

To illustrate, we will make x the subject. If we take the first equation and make x the subject, we will re-arrange the numbers and simplify to show that: x = (4y - 4) / 2

x = 2y - 2

Now we can plug this back into the second equation to replace the x with 2y - 2.  This shows that 3y + 3 =  3 (2y - 2)

3y + 3 = 6y - 6

3 + 6 = 6y - 3y

9 = 3y

So y = 9 / 3

y = 3

Now it is time to substitute this value back into one of the two equations...

If y = 3, 2x + 4 = 4 (3)

2x + 4 = 12

2x = 8

x = 8 / 2

x = 4