A system of equations has infinitely many solutions when the two
lines representing the equations coincide. i.e. the two equations are
the same or a multiple of each other.
Example of an equation that will form a system of equations with y = 5x - 3 such that the system will have infinitely many solutions is 2y - 10x = -6
For a system of linear equations to have no
solution, the lines representing the equations must be parallel but not coincide, i.e. they must have the same slope.
Example of an equation that will form a system of equations with y = 5x - 3 such that the system will have no solution is 2y = 10x
Otherwise, the system will have one solution.
Example of an equation that will form a system of equations with y = 5x - 3 such that the system will have one solution is 6y = 2x - 6
