Terms
Triangular System: n equations and n variables, like this example where n=3 \begin{align*} 2x_1 - 2x_2 + 3x_3 &= 3 \\ 3x_2 + 2x_3 &= 21 \\ 5x_3 &= 15 \end{align*}
Echelon System: A system of m linear equations in n variables is called an echelon system if. m ≤ n. Every variable is the leading variable of at most one equation. Every leading variable is to the left of the leading variables of all lower equations. \begin{align*} 6x_1 + x_2 - 3x_4 &= 11 \\ 3x_2 - 4x_3 + 5x_4 &= 6 \\ 2x_3 - 4x_4 &= -3 \end{align*}
Back Substitution: The intuitive method of solving a triangular system, going from the bottom to the top so that the equation with one variable is solved first.