1. Consistent and Independent System - This type of system has one unique solution, which can be represented by a point where the two lines intersect. The two lines have different slopes and y-intercepts, and they intersect at one point. This means that there is a unique solution for both equations. The graph of this system is a single point.
2. Inconsistent System - This type of system has no solution, which means that the two lines do not intersect. The two lines have different slopes and y-intercepts, and they are parallel to each other. This means that there is no solution that satisfies both equations. The graph of this system is two parallel lines that do not intersect.
3. Consistent and Dependent System - This type of system has infinitely many solutions, which means that the two lines are the same line. The two equations have the same slope and y-intercept, and they overlap each other. This means that there are infinitely many solutions that satisfy both equations. The graph of this system is a single line that overlaps itself.
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Answer:
1. Consistent and Independent System - This type of system has one unique solution, which can be represented by a point where the two lines intersect. The two lines have different slopes and y-intercepts, and they intersect at one point. This means that there is a unique solution for both equations. The graph of this system is a single point.
2. Inconsistent System - This type of system has no solution, which means that the two lines do not intersect. The two lines have different slopes and y-intercepts, and they are parallel to each other. This means that there is no solution that satisfies both equations. The graph of this system is two parallel lines that do not intersect.
3. Consistent and Dependent System - This type of system has infinitely many solutions, which means that the two lines are the same line. The two equations have the same slope and y-intercept, and they overlap each other. This means that there are infinitely many solutions that satisfy both equations. The graph of this system is a single line that overlaps itself.