Consider the following linear programming problem:
$$\begin{align} \text{min }& c^Tx \\ \text{subject to }& \left[ {\begin{array}{cccccccc} A_{11} & A_{12} & A_{13} & A_{14} & 0 & 0 & 0 & 0 \\ A_{21} & A_{22} & A_{23} & A_{24} & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\ \end{array} } \right] \left[ {\begin{array}{c} x_1\\ x_2\\ x_3\\ x_4\\ x_5\\ x_6\\ x_7\\ x_8 \end{array} } \right] = \left[ {\begin{array}{c} b_1\\ b_2\\ 5\\ 5\\ 5\\ 5\\ \end{array} } \right];\quad x_{1:8}\geq 0 \end{align}$$
Prove that $x* = (x_1,x_2,0,5)$ is a basic feasible solution to this problem.
NOTE: You can assume $A_{11}A_{22}-A_{12}A_{21}\ne0$.
I understand that given the form of this question $x_5, x_6, x_7, x_8$ are likely slack variables and so don't need to appear in a BFS. However, I can't figure out how to solve for $x_1, x_2$ without knowing any of the $A_{ij}$ or $b_1,b_2$ values since I imagine they're important to making sure $x_1,x_2\in[0,5]$.
Any help is appreciated!