There are 3 possible outcomes when solving simultaneous linear equations: (a) There is a unique solution (a, b). This is seen graphically as an intersection of the 2 lines, (b) There are no solutions. This is represented graphically as 2 parallel lines, and lastly (c) There are infinitely many solutions (Indeterminate) as the 2 lines are actually the same line.
Use the applet below to try to create those 3 possible outcomes. Move the sliders a to f to change the 2 equations.