Here is a set of five expressions: $$(x + y) \quad (x + 2y) \quad (x - 2y) \quad (x + 4y) \quad (2x + 3y)$$
Choose any pair of expressions and add together multiples of each (like Colin did).
Can you find a way to get an answer of $5x+8y$ in each case?
Warning... you will have to multiply the expressions by fractions in some cases.
If you're struggling to get started... take a look below to see how Charlie and Alison thought about the problem when combining multiples of $(x+2y)$ and $(2x+3y)$.
Charlie's trial and improvement approach:
Charlie chose a value for $a$ and worked out the value of $b$ that gave $5x$.
He then kept adjusting the values of $a$ and $b$ until he also got $8y$: