Question

Consider the system of equations

2x₁+x₂+4x₃=11

3x₁+x₂+5x₃=14

feasible solution is x₁=2,x₂=3,x₃ =1.Reduce this feasible solution to a basic feasible solution.

Answer 1

$2x_1+x_2=11-4x_3$

$3x_1+x_2=14-5x_3$

$\Delta=\begin{vmatrix} 2 & 1 \\ 3 & 1 \end{vmatrix}=-1$

$\Delta_1=\begin{vmatrix} 11-4x_3 & 1 \\ 14-5x_3 & 1 \end{vmatrix}=x_3-3$

$\Delta_2=\begin{vmatrix} 2 & 11-4x_3 \\ 3 & 14-5x_3 \end{vmatrix}=2x_3-5$

$x_1=\Delta_1/\Delta=3-x_3$

$x_2=\Delta_2/\Delta=5-2x_3$