> [!summary] A dependent variable is a variable in a reduced system of linear system with a leading 1. >[!info]+ Read Time **⏱ 1 min** # Definition A dependent variable is a variable in a system of [[Linear Equations|linear equations]] that is solved in terms of other variables (such as [[Free Variables|free variables]]). When a system of linear equations is reduced, a dependent variable will have a [[Leading 1s|pivot]]. # Examples > [!example] Finding the dependent variable in a reduced linear system > Given the augmented matrix in [[Reduced Row Echelon Form|reduced row echelon form]]: > $ \left[ \begin{array}{ccc|c} \color{blue}{1} & 0 & {2} & 3 \\ 0 & \color{blue}{1} & {-1} & 4 \\ 0 & 0 & {0} & 0 \\ \end{array} \right] > $ The blue entries are a dependent variable they have their own leading ones in a reduced system --- > 🧪 Think this could help someone else? [Star Math & Matter on Github](https://github.com/rajeevphysics/Obsidian-MathMatter) to help more learners discover it. ---