Solve The Following System of Linear Equations With An Additional Parameter

Today, Connor asked the following question involving a system of linear equation with an additional parameter :

Given that $x_1 + hx_2 = 4$  and $3x_1 + 6x_2 =8$, find all pairs of the form $(x_1,x_2)$ satisfying both equations.


OK…What do we do with that additional $h$? Well, read on!