Why do this problem?

On the one hand this problem is a simple exercise in solving pairs of linear simultaneous equations but on the other it provides perhaps unexpected results that call for investigating the connection between the algebra and geometry, and considering the equations of the lines and gradients.

Possible approach

Set this as homework or as a lesson starter and have a class discussion about the results.

Key questions

Why are the solutions of the two pairs of simultaneous equations so different when the equations are so nearly the same?