Asked to find the dual of a given primal problem. (Is my solution wrong? Solutions included)

Question

I'm not understanding how there can be two separate solutions to this problem. I've doubled checked and followed all the steps but I'm assuming my answer is wrong but similar?

Sorry, I don't have the reputation to embed:

Here is the original question, write the Dual of this System:

Here is the solution to this problem:

Here is my Solution:

Answer 1

Let $y_1 = -p_1$, $p_2=y_2, p_3=y_3$ and $y_4$ as the surplus variable and your formulation are equivalent.

By viewing $x_1 \le 0$ as a signed constraint rather than a regular constraint, you can actually save a variable, i.e. the formulation given in the book.