Simultaneous equations Yes, I know weve done this but you were a little ropey last week.

4 ways of solving them

1 Guessing the answers. Pros If you guess well, then easy to solve. Cons Hard to show your working. Only works for really simple ones. Can take a lot of time.

2 By adding/subtracting equations (traditional method) Pros Works for all but the most complicated equations( A – level). Will give exact answer. Cons Need to show all working and work carefully. May need to multiply equations first

3 Graphically Pros Will work every time Works for families of equations Cons Not always accurate Time consuming Long-winded, lots of room for mistakes to creep in.

4 Substitution Pros Can be quickest way Best way for complicated equations e.g.. powers Cons Not suitable for all equations More likely you are looking at A – level paper.

Traditional approach

2x + 2y = 8 3x – y = 16 Number equations 2x + 2y = 8 3x – y = 16 Make ys the same by multiplying x 2 6x – 2y =

2x + 2y = 8 3x – y = 16 2x + 2y = 8 Same no. of ys in 3x – y = 16 6x – 2y = 32 DIFFERENT signs so ADD + 8x = 40 x =

2x + 2y = 8 3x – y = 16 2x + 2y = 8 3x – y = 16 Substitute x = 5 in (easiest) 2 x 5 + 2y = y = 8 2y = -2 y =

Almost there

2x + 2y = 8 3x – y = 16 We have x = 5 and y = -1 so now we CHECK IT Check in because we havent used that yet (3 x 5) – (-1) = = = 16 2

And finally….. Dont forget to write your answers down clearly x = 5 and y = -1