Linear Algebra - Fundamental Principles

Fundamental principles

An equation is only true for certain values of the variables called solutions, or roots, of the equation. When it is desired that certain values of the variables make two or more equations true simultaneously (at the same time), the equations are called simultaneous equations and the values that make them true are called solutions to the system of simultaneous equations.

The graph of a linear equation, in a rectangular coordinate system, is a straight line, hence the term linear. The graph of simultaneous linear equations is a set of lines, one corresponding to each equation. The solution to a simultaneous system of equations, if it exists, is the set of numbers that correspond to the location in space where all the lines intersect in a single point.