ContourPlot[{1.5 x^2 + 2 x y - 1.5 y^2}/5, {x, -10,10}, {y, -10, 10}, ContourStyle -> {Red}, Frame -> False,Axes -> True, ContourShading -> None,PlotLegends -> {"\[Psi](x,y)"}]
ContourPlot[{x^2 - 3 x y - y^2}/5, {x, -10,10}, {y, -10, 10}, ContourStyle -> {Dashed}, Frame -> False,Axes -> True, ContourShading -> None,PlotLegends -> { "\[Phi](x,y)"}]
Show[%%,%]

contour[expr_, color_] :=
ContourPlot[expr, {x, -10, 10}, {y, -10, 10}, ContourStyle -> color,
  ContourShading -> None]

Show@MapThread[
   contour, {{1.5 x^2 + 2 x y - 1.5 y^2, x^2 - 3 x y - y^2}/5, {Red,
     Dashed}}] /.
Graphics[a__] :>
  Legended[Graphics[a],
   Placed[LineLegend[{Red, Dashed}, {"\[Psi](x,y)", "\[Phi](x,y)"}],
    After]]