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  "body": "\n## Definition\n\nLet $F$ be a field and let $n \\ge 1$ be an integer.\nA *linear equation* over $F$ in the unknowns $x_1, \\dots, x_n$ is an equation of the form\n$$a_1 x_1 + a_2 x_2 + \\cdots + a_n x_n = b,$$\nwhere the coefficients $a_1, \\dots, a_n$ are elements of $F$. The constant term $b$ is also an element of the field.\nA *solution* of the equation is a tuple $(s_1, \\dots, s_n) \\in F^n$ such that $a_1 s_1 + \\cdots + a_n s_n = b$.\n\n## Remarks\n\nThe equation $2x + 3y = 6$ over $\\R$ is linear, and $(3, 0)$ is a solution.\nThe equation $xy = 1$ is not linear, because it has a product of two unknowns.\nOver $\\R$ with $n = 2$, the solutions of a linear equation with $(a_1, a_2) \\ne (0, 0)$ form a line in the plane.\n\n## Explanations\n\n### L1 human\n\nA linear equation adds up the unknowns, each one times a fixed number, and sets the sum equal to a fixed number.\nNo unknown is squared, and no two unknowns are multiplied together.\nWith two unknowns over the real numbers, the solutions usually draw a straight line, and this gives the name \"linear\".\n",
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