Using vpasovle to search along a line

So I'm trying to solve a system of two variable equations (let's say x and y) over a varying parameter set using vpasolve. The equations are quite intricate and as such vpasolve frequently returns NaN or empty structures. However, I do know that the solutions generally reside along a fixed ratio s.t. where p ranges from 1 to 2.5. Can I specify this when using vpasolve? Is there any other way to go about this?

Answer 1

[John D'Errico]

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.

[Abdel Halloway]

Okay, so can I then restrict the range of p such that is only searches for p between 1 and 2.5?

[Walter Roberson]

https://www.mathworks.com/help/symbolic/vpasolve.html#bt5sqi5-1-init_guess