Core Algorithms

Find Parametrized Real Solutions of Systems of Equations 

Real solutions of for seven values of parameter .

In[1]:=

X sol = {x, y, z} /. Solve[x^2 + y^2 == z^2 && x + y + a z == 1, {x, y}, Reals]; Show[{ContourPlot3D[ x^2 + y^2 == z^2, {x, -1, 1}, {y, -1, 1}, {z, 0, 1}], Table[ParametricPlot3D[Tooltip[sol], {z, 0, 1}, PlotStyle -> {{Thickness[0.01], Hue[0.12 a]}}], {a, 7}]}, ViewPoint -> {-2, 2, -10}, Boxed -> False, Axes -> False]

Out[1]=