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Basic terminology

Created over 8 years ago, updated 24 days ago

Definition: A linear equation is an equation that can be written in the form

$$a_1 x_1 + a_2 x_2 + \cdots + a_n x_n = b$$

where $x_1, x_2, \ldots, x_n$ are variables (unknowns), $a_1, a_2, \ldots, a_n$ are constants called coefficients, and $b$ is a constant called the right-hand side or constant term.

The key property of a linear equation is that each variable appears only to the first power and is not multiplied by another variable, composed with a nonlinear function, or raised to any power other than 1.

Examples:

  • $2x + 3y = 6$ is linear
  • $x_1 - 4x_2 + x_3 = 0$ is linear
  • $x^2 + y = 1$ is not linear (variable squared)
  • $xy = 3$ is not linear (variables multiplied together)