Linear equation

In elementary algebra, linear equations are algebraic equations in which both sides of the equation are polynomials or monomials of the first degree - i.e. each term does not have any variables to a power other than one.

Form and Connection to Analytic Geometry

In general, a linear equation with $n$ variables can be written in the form $\displaystyle\sum_{i=1}^{n}a_ib_i=c$ , where $a_i$ is a series of constants, $b_i$ is a series of variables, and $c$ is a constant.

For the particular case $n=1$ , the resulting equation can be graphed as a point on the number line, and for the case $n=2$ (resulting in a linear function), it can be graphed as a line on the Cartesian plane, hence the term "linear" equation. This can extended to a general Cartesian n-space, in which the linear equation with the corresponding number of variables can be graphed as an n-1-space - this concept is the idea behind analytic geometry as envisioned by Fermat and Descartes.

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Linear equation

Contents

Form and Connection to Analytic Geometry

Systems, solutions and methods of solving

Variable Elimination

Matrices and Cramer's Law

See Also