A linear system is a set of equations that can be represented graphically as a straight line. It involves solving for the values of two or more variables that satisfy all of the equations in the system.
Linear systems can be used to solve a variety of real-world problems, such as finding the optimal solution for a business or engineering problem, determining the intersection point of two moving objects, or calculating the break-even point for a company.
There are several methods for solving linear systems, including substitution, elimination, and graphing. Each method has its own advantages and may be more suitable for certain types of problems.
Yes, a linear system can have one unique solution, no solution, or infinite solutions. This depends on the number of equations and variables in the system and whether the equations are consistent (have a solution) or inconsistent (have no solution).
A consistent linear system has at least one solution, while an inconsistent system has no solution. This can be determined by solving the system using any of the methods mentioned above, or by graphing the equations and seeing if they intersect at a point.