
Answering Simultaneous Equations
 
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

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.
