algebra 2 flashcards

Consistent vs. Inconsistent Systems:

A consistent system has at least one solution (intersecting lines or planes). An inconsistent system has no solutions (parallel lines or planes).

Dependent vs. Independent Systems:

A system is dependent if the equations are multiples of each other (representing the same line). It has infinitely many solutions. An independent system has a unique solution.

Solving Systems with Three or More Variables:

The substitution and elimination methods can be extended to systems with more variables, but the process becomes more complex. Matrix methods (Gaussian elimination, etc.) are often more efficient for larger systems.

Applications:

Systems of equations are used extensively in modeling real-world situations, such as mixture problems, supply and demand analysis in economics, and network analysis in computer science.