But the reasoning is total garbage, right?

It says the number of blue balls drawn is x and the number of red balls drawn is y, and then asserts x + y = 100, which is wrong.

Then it proceeds to "solve" an equation which reduces to x = x to conclude x = 0.

It then uses that to "prove" that y = 100, which is a problem as there are only 50 red balls in the container and nothing causes any more to be added.

It's like "mistakes bad students make in Algebra 1".