Reducing two equations to one

When one equation is linear, isolate a variable and substitute it into the other equation. Solve the resulting equation, then find the partner value from the same root. Write ordered pairs rather than two disconnected lists. Elimination also works when the repeated expression is nonlinear. For x2+y2=13 and x2-y2=5, adding gives 2x2=18; subtracting gives 2y2=8. All four pairs (+-3,+-2) satisfy both equations. Before dividing by an expression, establish that it is nonzero. For rational equations exclude every original zero denominator. Substitute each candidate pair into both original equations: squaring or clearing denominators can introduce invalid candidates.