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Infinitely many solutions
Infinitely many ordered pairs satisfy both equations. Graphically, the lines are coincident (the same line written in two forms).
No solution
No ordered pair satisfies both equations. Graphically, the lines are parallel (same gradient, different intercepts).
System of linear equations
A set of two or more linear equations involving the same variables, solved together to find values that satisfy every equation in the system.
Unique solution
Exactly one ordered pair $(x,y)$ satisfies both equations. Graphically, the two lines intersect at one point.