Is there a small mistake in the simplex solution from 2022 september?

Question

I thought the minus sign should not be there when we move y0 to the other side.

y2 + 5/3 y0 = 8/3 x1

Answer 1

We have y0 = 3/5*x0 + x1 and therefore x0 = 5/3*y0 - 5/3*x1. For the equation y2 = -x0 + x1, we therefore get 

    y2 = -x0 + x1 = y2 
       = -(5/3*y0 - 5/3*x1) + x1 
       = -5/3*y0 + 5/3*x1 + x1
       = -5/3*y0 + 8/3*x1

So, the example solution is correct, isn't it?

Comments

I agree with that until there.
y2 = -5/3*y0 + 8/3*x1
Then, we see that the constraint for y2 is violated:
0 <= y2 := -5
Until now everything makes sense for me. I thought there is an issue in the pivoting step.

We pivot x1 with y2 to set y2 = 0:

                    y2 = -5/3*y0 + 8/3*x1       | + 5/3*y0
      5/3*y0 + y2 = 8/3*x1                      | *3/8
5/8*y0 + 3/8*y2 = x1
       
in the exam solution pdf it is written: x1 = -5/8*y0 + 3/8*y2 (Note the minus sign)
Am i mixing something up here?

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Yes, you are right, now I see the problem, and that was indeed a typo. It has been fixed now. Thanks for pointing it out!