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lang-mma
MeshFunctionsone can directly plot the solution with a "one-liner"ContourPlot[{f[x, y], g[x, y]}, {x, 0, 2}, {y, -1, 1}, MeshFunctions -> {f[#1, #2] - g[#1, #2] &}, Mesh -> {{0}}, MeshStyle -> Directive[Red, PointSize[Large]]]$\endgroup$