: Mathématiques: linear equation

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linear equation

In mathematics, a linear equation is an equation that may be put in the form ${\\displaystyle a_{1}x_{1}+\\ldots +a_{n}x_{n}+b=0,}$ where ${\\displaystyle x_{1},\\ldots ,x_{n}}$ are the variables (or unknowns), and ${\\displaystyle b,a_{1},\\ldots ,a_{n}}$ are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients ${\\displaystyle a_{1},\\ldots ,a_{n}}$ are required to not all be zero. Alternatively, a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken. The solutions of such an equation are the values that, when substituted for the unknowns, make the equality true.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Linear_equation)