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Definition: A linear equation in the n variables x_1, x_2, … , x_n is an equation that can be written in the form (a_1)(x_1) + (a_2)(x_2) + ... + (a_n)(x_n) = b where the coefficients a_1, a_2, … , a_n and the constant term b are constants.
Source: Linear Algebra: A Modern Introduction, 3rd edition by David Poole (note-custom edition titled Matrix Algebra)