Find all degenerate basic feasible solution of the system

Question

$$x_1 + x_2 + x_3 = 3$$ $$x_1 − x_2 + x_4 = 0$$ $$x_1, x_2, x_3, x_4 ≥ 0$$

How should I proceed it ?

Should I convert it to 2-D like this $$x_1 + x_2 \leq 3$$ $$x_1 − x_2 \leq 0$$ ? What would be my next steps ?

Answer 1

A basis has two basic variables, so you're looking for solutions where at least three of the variables are $0$, and at most one is nonzero. Obviously you can't have all four $0$, so there must be exactly one nonzero. That one can't be $x_1$ or $x_2$ or $x_4$, as that would make the second equation false, so it must be $x_3$.