What is referred to as a system of equations where all equations are linear?

A system of equations where all equations are linear is referred to as a system of linear equations. This means that each equation in the system represents a straight line when graphed in a coordinate plane, and these equations consist of constants and linear variables, typically in the form of ( ax + by = c ).

The linearity of the equations is essential, as it allows for straightforward methods of solving such systems, such as substitution, elimination, or using matrices. Additionally, these systems can have various types of solutions: one unique solution (intersecting lines), no solutions (parallel lines), or infinitely many solutions (coincident lines).

Understanding the concept of a system of linear equations is crucial in both theoretical mathematics and practical applications, such as in physics, economics, and engineering, as they form the foundation for many problems and predictive models.