- #1
nhrock3
- 415
- 0
why lenear system has a single solution?
A linear system is a set of linear equations that are related to each other. Linear equations are mathematical expressions that involve variables raised to the first power and are graphically represented as straight lines. When these equations are combined, they form a system that can be solved to find the values of the variables that satisfy all of the equations.
Linear systems are used in many real-world applications, such as in engineering, economics, and physics. Understanding how to solve linear systems allows us to analyze and make predictions about these systems, which can help us make informed decisions.
A single solution in a linear system means that there is only one set of values for the variables that satisfies all of the equations in the system. This is significant because it tells us that the system has a unique solution and there is no ambiguity in the values of the variables.
If a linear system has no solution, it means that there is no set of values for the variables that satisfies all of the equations in the system. In other words, the lines representing the equations do not intersect, and there is no point that satisfies all of the equations at the same time. This could happen when the equations are parallel or when they represent contradictory statements.
The number of solutions in a linear system can be determined by graphing the equations and looking at the intersection of the lines. If the lines intersect at one point, there is a single solution. If the lines are parallel, there is no solution. If the lines overlap, there are infinitely many solutions. Alternatively, the number of solutions can also be determined by solving the system algebraically using techniques such as substitution or elimination.