Were you surprised by your answers?

Explain why the solutions are so different and yet the pairs of equations are nearly identical.

Solve the two pairs of simultaneous equations
\[\begin{align*}
x + 0.99999y &= 2.99999 \\
0.99999x + y &= 2.99998
\end{align*}\]
and
\[\begin{align*}
x + 1.00001y &= 2.99999 \\
0.99999x + y &= 2.99998.
\end{align*}\]

Were you surprised by your answers?

Explain why the solutions are so different and yet the pairs of equations are nearly identical.