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Answering Simultaneous Equations
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Let's see how you got on:
- 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
- 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
- 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
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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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