It sounds as if you know the solutions lie along a line, but you don't know the slope of that line, that x and y must be proportional to each other.
You really don't have variables x and y here then. Substitute for x as x = p*y.
This leaves you with two variables, p and y. You still have two equations, in the two unknowns. Once you solve them for p and y, you can then recover x. Since p and y solved the two equations, the recovered x and y will be solutions to the original equations.
