# Definition of solution to a linear equation

Put content here**Definition:** A **system of linear equations** (or **linear system**) is a finite collection of linear equations involving the same set of variables $x_1, x_2, \ldots, x_n$:
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$$\begin{cases}\n a_{11} x_1 + a_{12} x_2 + \cdots + a_{1n} x_n = b_1 \\\n a_{21} x_1 + a_{22} x_2 + \cdots + a_{2n} x_n = b_2 \\\n \quad\vdots \\\n a_{m1} x_1 + a_{m2} x_2 + \cdots + a_{mn} x_n = b_m\n\end{cases}$$
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This can be written compactly in matrix form as $Ax = b$, where:
- $A$ is the $m \times n$ **coefficient matrix**
- $x$ is the column vector of variables
- $b$ is the column vector of constants
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**Example:**
$$\begin{cases}\n2x + y = 5 \\\nx - 3y = -1\n\end{cases}$$
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is a system of 2 equations in 2 unknowns.

# Parents

* Basic terminology