**Back-Substitution**

The process of solving a linear system of equations that has been transformed into row-echelon form or reduced row-echelon form. The last equation is solved first, then the next-to-last, etc.

Example: | Consider a system with the given row-echelon form for its augmented matrix. The equations for this system are \(\eqalign{x - 2y + z &= 4\\y + 6z &= - 1\\z &= 2}\) The last equation says \(\eqalign{y + 6\left( 2 \right) &= - 1\\y &= - 13}\) Now substitute \(\eqalign{x - 2\left( { - 13} \right) + \left( 2 \right) &= 4\\x &= - 24}\) Thus the solution is |

**See also**

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