## What is a system of linear equations

### A system of linear equations is a collection of two or more linear equations that are to be solved simultaneously

A system of linear equations is a collection of two or more linear equations that are to be solved simultaneously. Each equation in the system represents a relationship between unknown variables, and the goal is to determine the values of those variables that satisfy all of the given equations. The solutions to the system are the values of the variables that make every equation in the system true.

A general system of linear equations can be written in the form:

a₁x₁ + a₂x₂ + … + aₙxₙ = b₁

a₁x₁ + a₂x₂ + … + aₙxₙ = b₂

…

a₁x₁ + a₂x₂ + … + aₙxₙ = bₘ

where x₁, x₂, …, xₙ are the unknown variables, a₁, a₂, …, aₙ are the coefficients of the variables, and b₁, b₂, …, bₘ are the constants on the right-hand side of each equation.

The system can have multiple solutions, a unique solution, or no solution at all. These possibilities depend on the relationships between the equations and the number of unknown variables. The methods for solving systems of linear equations include substitution, elimination, and matrix methods such as Gaussian elimination and matrix inversion.

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