# Definition of coefficients of a linear equation

Put content here**Definition:** A **solution** to a linear equation $a_1 x_1 + a_2 x_2 + \cdots + a_n x_n = b$ is an ordered $n$-tuple of numbers $(s_1, s_2, \ldots, s_n)$ such that when each $x_i$ is replaced by $s_i$, the equation holds true:
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$$a_1 s_1 + a_2 s_2 + \cdots + a_n s_n = b$$
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In other words, substituting the solution values into the equation produces a valid equality.
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**Example:** For the equation $2x + 3y = 6$:
- $(3, 0)$ is a solution because $2(3) + 3(0) = 6$ ✓
- $(0, 2)$ is a solution because $2(0) + 3(2) = 6$ ✓
- $(1, 1)$ is **not** a solution because $2(1) + 3(1) = 5 \neq 6$ ✗
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A single linear equation in two or more variables has infinitely many solutions.

# Parents

* Basic terminology