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

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4 ways of solving them

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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.

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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

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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.

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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.

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Traditional approach

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2x + 2y = 8 3x – y = 16 Number equations 2x + 2y = 8 3x – y = 16 Make ys the same by multiplying x 2 6x – 2y = 32 1 2 23

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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 = 5 1 2 1 3 31 3

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2x + 2y = 8 3x – y = 16 2x + 2y = 8 3x – y = 16 Substitute x = 5 in (easiest) 2 x 5 + 2y = 8 10 + 2y = 8 2y = -2 y = -1 1 2 1

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Almost there

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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) = 15 - - 1 = 15 + 1 = 16 2

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

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Simultaneous Equations. Aims for this topic: You will know what simultaneous equations are You will be able to solve simultaneous equations using graphs.

Simultaneous Equations. Aims for this topic: You will know what simultaneous equations are You will be able to solve simultaneous equations using graphs.

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