Rule 1:
If the solution of two equations is like 2=7, then the equations are not equilateral with no common solution.
Rule 2:
If the solution of two equations is like 0=0, then the equations are equilateral with infinite common solution.
Rule 3:
If the solution of two equations is like 2=2 or 7=7 or 9=9, then the equations have only one solution.
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