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Definition: A solution of of a linear equation (a_1)(x_1) + (a_2)(x_2) + ... + (a_n)(x_n) = b of a vector [s_1, s_2, … , s_n] whose components satisfy the equation when we substitute x_1 = s_1. x_2 = s_2, … , x_n = s_n. A solution of a system of linear equations is a vector that is simultaneously a solution of each equation in the system.
Source: Linear Algebra: A Modern Introduction, 3rd edition by David Poole (note-custom edition titled Matrix Algebra)