GCSE Maths

Answering Simultaneous Equations

Let's see how you got on:
  1. 2a + b = 21
    a + 2b = 24

    Rearrange one of the equations: b = 21 - 2a
    Next substitute in the other: a + 2(21 - 2a) = 24
    Solve: a + 42 - 4a = 24
    Rearrange: 42 - 24 = 3a
    Answer: a = 6
    Finally substitute: b = 21 - 2×6
    Answer: b = 9
     

  2. 5p + q = 100
    2p - q = -30

    Rearrange one of the equations: q = 100 - 5p
    Next substitute in the other: 2p - (100 - 5p) = -30
    Solve: 2p - 100 + 5p = -30
    Rearrange: 7p = 70
    Answer: p = 10
    Finally substitute: q = 100 - 5×10
    Answer: q = 50
     

  3. m + n = 0
    6m - n = 49

    Rearrange one of the equations: m = -n
    Next substitute in the other: 6(-n) - n = 49
    Solve: -7n = 49
    Answer: n = -7
    Finally substitute: m = -(-7)
    Answer: m = 7

If you managed to get all three of the above right, you have done well! If not, take a close look at the workings above, then try them again. There are always several ways of rearranging each pair of equations.


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