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a new variable, ''y''<sub>1</sub>, is introduced with
:<math> \begin{align} y_1 = x_1 - 5\\x_1 = y_1 + 5 \end{align}</math>
The second equation may be used to eliminate ''x''<sub>1</sub> from the linear program. In this way, all lower bound constraints may be changed to non-negativity restrictions.
Second, for each remaining inequality constraint, a new variable, called a ''slack variable'', is introduced to change the constraint to an equality constraint. This variable represents the difference between the two sides of the inequality and is assumed to be nonnegative. For example the inequalities
:<math> \begin{align}
x_2 + 2x_3 &\le 3\\
-x_4 + 3x_5 &\ge 2
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are replaced with
:<math> \begin{align}
x_2 + 2x_3 + s_1 &= 3\\
-x_4 + 3x_5 - s_2 &= 2\\
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