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

Do you have any strategies for solving simultaneous equations? How will you decide which to use here?

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

Other than as strings of symbols, how else can we represent these equations? What does a solution to the equations correspond to in this language?

Notice that each equation specifies a line. A solution to the two equations corresponds to a point on both lines. What do the lines look like?