Final answer:
In mathematics, the graphs of systems of equations can have different types of solutions. When a system of equations has exactly one solution, it can be represented graphically as two lines intersecting at a single point. When a system of equations has no solutions, it can be represented graphically as two parallel lines that never intersect. When a system of equations has infinitely many solutions, it can be represented graphically as two identical lines overlapping.
Step-by-step explanation:
In mathematics, the graphs of systems of equations can have different types of solutions. When a system of equations has exactly one solution, it can be represented graphically as two lines intersecting at a single point. This occurs when the lines have different slopes and are not parallel.
When a system of equations has no solutions, it can be represented graphically as two parallel lines that never intersect. This occurs when the lines have the same slope but different y-intercepts.
When a system of equations has infinitely many solutions, it can be represented graphically as two identical lines overlapping. This occurs when the two equations represent the same line.