Consistency of linear system of equations

 A system of linear equations is a set of equations that can be written in the form Ax = b, where A is a matrix of coefficients, x is a vector of variables, and b is a vector of constants.

A system of linear equations is said to be consistent if it has at least one solution. This means that there exists at least one set of values for the variables x that satisfies all the equations in the system.

For example, consider the following system of linear equations:

2x + y = 5 x - 3y = -2

This system is consistent, because it has a unique solution: x = 1, y = 3.

On the other hand, consider the following system of linear equations:

2x + y = 5 2x + y = 6

This system is inconsistent, because there is no set of values for x and y that satisfies both equations.

To determine whether a system of linear equations is consistent, you can use various methods, such as graphing the equations, using substitution, or using elimination