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Published byJaden Hunter Modified over 4 years ago

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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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Solving Systems of Equations So far, we have solved systems using graphing and substitution. These notes show how to solve the system algebraically using.

Solving Systems of Equations So far, we have solved systems using graphing and substitution. These notes show how to solve the system algebraically using.

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