Finding equilibria of coupled differential equations requires solving simultaneous equations. The following are linear equations, where the only possibilities are no solutions, one solution, or a whole line of solutions. For each of the following pairs, solve each equation for y in terms of x, set the two equations for x equal, and solve for x. Check that both equations give the same value for y. Sketch a graph with y on the vertical axis.
8 - 2y + 4x = 0
-2 + y - 2x = 0
What goes wrong? Use your graph with y on the vertical axis to explain the problem.