Suppose the variable x1 can assume any real value. Show that the following substitution...

Suppose the variable x₁ can assume any real value. Show that the following substitution using nonnegative variables x₂ and x₃ permits x₁ to assume any real value.

x ₁ = x₂ − x₃, where x₁ is unconstrained

and

Thus, if a computer code allows only nonnegative variables, the substitution allows for solving the linear program in the variables x₂ and x₃ and then recovering the value of the variable x₁.