When we think of addition, usually it involves something like this:

This is in fact the addition of constants, 3 never changes, 7 never changes and so the answer of 10 can never change (ignore any temptation to consider bases, at least not just yet!), whereas if we look at the equation below:

The situation is somewhat different. 10 is constant and can never change but X and Y can have an infinite range of values respectively, provided of course that they complement each other by adding up to 10:

Coefficients

OK, so what if we have more than one ‘X’?


This means “four times X” but because X is a variable we can’t write the result as another entity (such as 10, because we wouldn’t leave ‘3+7’ as it is, we’d say ‘10’).

The number ‘4’ in this case is called the ‘Coefficient of X’

Can we add these together? – Well provided that we have ‘like terms’ then yes, we can:

We can collect ‘like terms’ and simplify, buy if we have different variables we can’t simplify:


It can’t go any further, the answer is 4x+8y – end of!