Solve the two pairs of simultaneous equations:
x + 0.99999y
=
2.99999
0.99999x + y
=
2.99998
and
x + 1.00001y
=
2.99999
0.99999 x + y
=
2.99998.
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.