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Solve the two pairs of simultaneous equations:
\begin{eqnarray} x + 0.99999y & = & 2.99999 \\ 0.99999x + y
& = & 2.99998 \end{eqnarray} and \begin{eqnarray} x +
1.00001y & = & 2.99999 \\ 0.99999 x + y & = &
2.99998. \end{eqnarray}
Explain why the solutions are so different and yet the pairs of
equations are nearly identical.
NOTES AND BACKGROUND
In this question a small perturbation in one of a pair of equations
makes a big change in the solutions. Considering the geometrical
properties of the lines represented by the equations helps to
de-mystify the results.