How to draw several contours label in separate colors

Question

Good morning. I have two equations (or more) that I want plot with ContourPlot colored with different colours and labelled according to equation order, in a automatic way. I have tried several solutions without success. My plot should remain as

g1 = x + 2 y; g2 = 2 x + y; b = {2, 2};
grosor = Thickness[0.01];
color3 = Blue;
color4 = Magenta;

coloresRest = {Blue, Magenta}; 
labelRest = Table[Text[Style["(" <> ToString@i <> ")", coloresRest[[i]]]], 
 {i, Length@coloresRest}];

ContourPlot[{g1 == b[[1]], g2 == b[[2]]}, {x, -2, 4}, {y, -2, 4}, 
  Frame -> False, Axes -> True, 
  ContourStyle -> Thread[{coloresRest, grosor}], 
  Epilog -> {Text[Style["(1)", color3], Offset[{20, 0}, {-2, 2}]], 
     Text[Style["(2)", color4], Offset[{-10, -10}, {-1, 4}]]}, 
  ImageSize -> 400]

I have tried with Table, ContourLabel, Riffle or Epilog, without success. For example:

ContourPlot[{g1 == b[[1]], g2 == b[[2]]}, {x, -2, 4}, {y, -2, 4}, 
  Frame -> False, Axes -> True, 
  ContourStyle -> Thread[{coloresRest, grosor}], 
  ContourLabels -> Table[Text[Style[labelRest[[i]], Offset[{10, 0}, {#1, #2} &]]], 
   {i, 1, Length@coloresRest}], 
  ImageSize -> 400]

or

ContourPlot[{g1 == b[[1]], g2 == b[[2]]}, {x, -2, 4}, {y, -2, 4}, 
  Frame -> False, Axes -> True, 
  ContourStyle -> Thread[{coloresRest, grosor}], 
  ContourLabels -> {Riffle[coloresRest, Inset[labelRest, Offset[{10, 0}, {#1, #2} &]]]}, 
  ImageSize -> 400]

I realize that expresión {#1, #2}& yield coordinates for labels, chosen by Mathematica. I'd prefer that and not to choose such coordinates.

Thank in advance

---

Sorry, but I forgot that

grosor=Thickness[0.01]
color3=Blue
color4=Magenta

and I prefer that Mathematida choose coordenates of label with {#1, #2} & instruction.

Thank

Answer 1

Update: As an alternative and more flexible approach, we can post-process ContourPlot output to inject contour labels.

ClearAll[addLabels]
addLabels[colors_, labels_: Automatic, threshold_: 1/3][g_Graphics] :=
  Module[{diag = ArcLength@Line[Transpose @ PlotRange @ g], 
   assoc = AssociationThread[colors, 
     labels /. Automatic -> 
       MapIndexed[Framed[Style["(" <> ToString@#2[[1]] <> ")", #, 12], 
        FrameStyle -> None, Background -> White, FrameMargins -> Small] &, colors]]}, 
  ReplaceAll[{d_Directive, l__Line} :> {d, l, 
     Module[{BSF = BSplineFunction[First@#], 
        pos = If[ArcLength[#] < diag threshold, {.5}, 
         If[Norm[Subtract @@ #[[1, {1, -1}]]] <= 
           diag threshold, {.3, .8}, {0, 1}]]}, 
       Text[assoc@FirstCase[d, _?ColorQ], #] & /@ (BSF /@ pos)] & /@ {l}}] @ Normal[g]]

addLabels[colors_, labels_: Automatic, threshold_: 1/3][Legended[g_, legend_]] := 
 Legended[addLabels[colors, labels, threshold] @ g, legend]

The first argument, colors, is a list of colors with the same length as functionlist in ContourPlot[functionlist,...].

The (optional) second argument, labels, is a list of labels with the same length (if this argument is Automatic or not provided, the labels are taken to be numbers from 1 to length of colors).

The third argument, threshold, is also optional and it is used to control the number of labels and label positions on a contour curve. If a contour curve is too short (in comparison to the length of the diagonal of the plotting area) then a single label is placed in the middle of the curve. If the start and end points of the curve not too close two labels are placed at the two ends of the curve. If they are too close (as in a closed curve) two labels are placed so that they are not too close to each other.

We can use addLabels in two ways: (1) as the the setting for the option DisplayFunction by adding the option DisplayFunction -> addLabels[colors, labels, threshold] to ContourPlot, or (2) by wrapping ContourPlot[...] with it, i.e., using addLabels[colors, labels, threshold] @ ContourPlot[...].

Examples:

{g1, g2, b} = {x + 2 y, 2 x + y, {2, 2}};

funcs = {g1 - b[[1]], g2 - b[[2]]};

colors = {Blue, Magenta};

options = {Frame -> False, Axes -> True, ContourShading -> None, 
   ImageSize -> 400, PlotRangePadding -> Scaled[.05]};

ContourPlot[funcs, {x, -2, 4}, {y, -2, 4}, 
 Evaluate @ options, 
 ContourStyle -> Thread[Directive[colors, Thick]], 
 DisplayFunction -> addLabels[colors]]

addLabels[colors] @ ContourPlot[funcs, {x, -2, 4}, {y, -2, 4}, 
     Evaluate @ options, ContourStyle -> Thread[Directive[colors, Thick]]]

 same picture

With

funcs = {g1 - b[[1]], g2 - b[[2]], Cos[x - 1] + Cos[y - 1] - 1/3, 
   Sin[ x - 1] + x y Cos[y + 1] - 1/4};

colors = {Blue, Magenta, Red, Green};

we get

We can use the second argument of addLabels to inject pre-specified labels instead of automatically generated ones:

labels = MapIndexed[Framed[Style["(" <> ToString@#2[[1]] <> ")", #, Bold, 18], 
     FrameStyle -> None, Background -> White] &, colors];

ContourPlot[funcs, {x, -2, 4}, {y, -2, 4},
 Evaluate @ options,
 ContourStyle -> Thread[Directive[colors, Thick]], 
 DisplayFunction -> addLabels[colors, labels]]

Add the option PlotLegends->"Expressions" to get

Original answer:

{g1, g2, b} = {x + 2 y, 2 x + y, {2, 2}};

colors = {Blue, Magenta};

labels = MapIndexed[Framed[Style["(" <> ToString@#2[[1]] <> ")", #, 18], 
     FrameStyle -> None, Background -> White] &, colors];

Show[MapThread[
      ContourPlot[#, {x, -2, 4}, {y, -2, 4}, 
         Frame -> False, 
         Axes -> True,
         ContourShading -> None, 
         Contours -> {0}, 
         ContourStyle -> Directive[#2, Thick], 
         ContourLabels -> Function[{x, y, z}, Text[#3, {x, y}]], 
         ImageSize -> 400] &, 
      {{g1 - b[[1]], g2 - b[[2]]}, colors, labels}]]