This
eqs = {3 x^2 + y^2 - 9 == 0, x^2 + y^2 - 1 == 0};
plots = ContourPlot[eqs, {x, -4, 4}, {y, -4, 4}]
gives a blank plot
This
eqs = {3 x^2 + y^2 - 9 == 0, x^2 + y^2 - 1 == 0};
plots = ContourPlot[Evaluate[eqs], {x, -4, 4}, {y, -4, 4}]
gives the desired plot
