**Echelon Method of Solving a Linear System**

**a.** If possible , arrange the equation so that these is an x_{1} – term in the first equation, an x_{2} –term in the second equation, and so on.

**b.** Eliminate the x_{1} –term in all equations after the first equation.

**c.** Eliminate the x_{2} –term in all equations after the second equation.

**d.** Eliminate the x_{3} –term in all equation after the third equation.

**e.** Continue in this way until the last equation has the form ax_{n} = k, for constants a and k, if possible.

**f.** Multiply each equation by the reciprocal of the coefficient of its first term.

**g.** Use back-substitution to find the value of each variable.