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Copy of Systems of linear equations

Solve the assigned system of linear equations, then type the lines equations in the r and s fields (press Enter to confirm each input), in order to view the graphical solution of the system.
Why is this kind of system named linear ? Which conditions allow you to decide a priori whether a system has a single unique solution / infinitely many solutions / no solution ? Write down on paper the equations of a system having a single unique solution, one with infinitely many solutions, and one having no solution.