Systems of equations can have just about any number of solutions: zero, one, two, etc., or even infinitely many solutions.
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If they are quadratic equations then if their discriminant is less than zero then they have no solutions
A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.
Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.
A single point, at which the lines intercept.