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Why do programs misbehave?

Example:

Solve the system: 12 x = 25 y

2 y = a x - 1

where the parameter a is computed from a previous section of the program.

For a = 1, the solution will be found as: x = 25

y = 12

A 3% error in the evaluation of a translates into a 400% error in the results:

For a = 0.97, the solution is: x = 100

y = 48

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