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The general form of factorising is that if we have ab+ac, we can rewrite this as a(b+c). We multiply each statement inside the bracket by a. So we’re effectively ripping out common terms. We are dividing ...

First we assign, for example, that x = cost of 1 book, and y = cost of 1 apple. Then we make these into simultaneous equations, such as: 3x+2y=19 (eqn. 1) and x+5y=15 (eqn. 2). Now multiply eqn. 2 to get ...

Key here is the order of operation.g(4) =2x4 - 5=8-5=3fg(4) = f(3)=15/3=5gf(-30)f(-30)=15/-30=-1/2gf(-30)=g(-1/2)=2x-1/2 -5=-1-5=-6gf(x)f(x)=15/xg(15/x)=2*15/x -5=30/x -5

3x+5y=224x-5y=6Our first task is to cancel out one of the variables. So you see that both y variables have a 5 before them. As one has -5 and the other has +5 you can add both simultaneous equations toget...

So there are 35 students in total. 10 which have both a laptop and a TV and 12 with only a TV. There are 20 students that own laptops. We have to find out how many students only have laptops. To do this w...