A system of linear equations is…
a collection of one or more linear equations involved the same variables.
A system of linear equations is a set of two or more linear equations with the same variables. These equations are written in the standard form of Ax + By = C, where A, B, and C are constants and x and y are the variables. The system is considered to be linear because the equations are first-degree, or linear, with no variables raised to a power greater than one.
The objective of solving a system of linear equations is to find the values of the variables that satisfy all the equations in the system. This is achieved by finding the solution, which is the point that satisfies all the equations in the system. There are three possible types of solutions to a system of linear equations: a unique solution, no solution, or infinitely many solutions. The solution type is determined by the relationship between the equations in the system.
Linear systems are used in a variety of fields, including physics, engineering, economics, and computer science, to model real-world situations. They are also used in optimization problems, where we seek to maximize or minimize a given objective function subject to linear constraints.
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