Q

QuestionMathematics

To classify the three types of systems of linear equations, we first need to understand the concept of the number of solutions a system can have. A system of linear equations can have zero, one, or infinitely many solutions. **Step 2:** The first type of system is called a **Consistent Independent System**. This system has a unique solution, which means there is only one set of values for the variables that satisfy all equations in the system. Geometrically, this represents a single point where the lines (or planes in 3D space) intersect. **Step 3:** The second type is a **Consistent Dependent System**. This system has infinitely many solutions because the equations are essentially the same, just written differently. In other words, every solution that satisfies one equation also satisfies the other equation(s). Graphically, this represents a whole line (or a plane in 3D space) of points. **Step 4:** The third type is called an **Inconsistent System**. This system has no solution since the equations contradict each other. Geometrically, this represents parallel lines (or planes in 3D space) that never intersect. **