Plot solutions of NSolve with multiple variables in different colors

Question

I'm trying to plot the solutions of a set of equations in dependence of a parameter. Say my variables are

vars = {x,y};

and the system I want to solve is

r[c_] := NSolve[Join[{{x (1 - (x + .5 y)/c), y (1 - (.5 x + y))} == {0, 
 0}}, {vars > 0}], vars];

This works but the curves have the same color

Plot[vars /. r[c], {c, 0, 3}]

This works but I have to call r[c] every time

Plot[{x /. r[c], y /. r[c]}, {c, 0, 3}]

I hoped to solve the problem with Evaluate but this doesn't work

Plot[Evaluate[vars /. r[c]], {c, 0, 3}]

NSolve::ratnz "NSolve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result."

In this case there's no plot.

I know it's kind of an aesthetic question but out of curiosity: is there a way to call r[c] only once and still get the curves in different colors?

Thanks!

Answer 1

Clear["Global`*"]

vars = {x, y};

r[c_] = Solve[Join[Thread[
     {x (1 - (x + y/2)/c), y (1 - (x/2 + y))} == {0, 0}],
    Thread[vars > 0], {0 <= c <= 3}], {x, y}] // Simplify

Plot[Evaluate[Tooltip[vars] /. r[c][[1]]], {c, 0, 3}, 
 AxesLabel -> {Style["c", 14, Bold], None},
 PlotLegends -> Placed[
   (Style[#, 14, Bold] & /@ vars), {.8, .3}]]