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Simultaneous equations

Simultaneous equations

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Simultaneous equations

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  1. Simultaneous equations Yes, I know we’ve done this but you were a little ropey last week.

  2. 4 ways of solving them

  3. 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. 1 Guessing the answers.

  4. 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 2 By adding/subtracting equations(traditional method)

  5. 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. 3 Graphically

  6. 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. 4 Substitution

  7. Traditional approach

  8. 2x + 2y = 83x – y = 16 Number equations 2x + 2y = 8 3x – y = 16 Make ‘y’s the same by multiplying x 2 6x – 2y = 32 1 2 2 3

  9. 2x + 2y = 83x – y = 16 2x + 2y = 8 Same no. of y’s in 3x – y = 16 6x – 2y = 32 DIFFERENT signs so ADD + 8x = 40 x = 5 1 1 3 2 3 1 3

  10. 2x + 2y = 83x – 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

  11. Almost there

  12. 2x + 2y = 83x – y = 16 We have x = 5 and y = -1 so now we CHECK IT Check inbecause we haven’t used that yet (3 x 5) – (-1) = 15 - - 1 = 15 + 1 = 16 2

  13. And finally….. Don’t forget to write your answers down clearly x = 5 and y = -1