> [!summary] A linear equation is an equation relating linear unknown variables and their constant with a solution value > **Key Equations:** > Linear Equation: $a_{1}x_{1} + a_{2}x_{2} \dots a_{n}x_{n}=b$ >[!info]+ Read Time **⏱ 1 min** # Definition Linear equations an equations whose unknown variables ($x$) are linear and are multiplied by some constant ($a_{n}$) and equal some solution value $(b_{n})$. An equation describes this to $x_{n}$ is denoted as $ a_{1}x_{1} + a_{2}x_{2} \dots a_{n}x_{n}=b $ A linear equation can be some $nth$ number of variable long. **Multiple linear equations** are called a **system of linear equations** with $m$ linear equation and $n$ variables written as $ \begin{align*} a_{1}x_{1} + a_{2}x_{2} \dots a_{n}x_{n} &=b_{1} \\ a_{21}x_{1} + a_{22}x_{2} \dots a_{2n}x_{n}&=b_{2} \\ \vdots\\ a_{m1}x_{1} + a_{m2}x_{2} \dots a_{mn}x_{n}&=b_{m} \end{align*} $