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[bigm]

Thanks Professor. Great explanation!👍❤

[sy]

Thank you for explaining. I think the problem condition requires "x, y, z: integers".
If not, concerning "finding ALL solutions", we cannot say there are only 2 solutions, judging from the 2 cases use "transforming from (1-y)(x-z) to 1-y=1, x-z=1 or 1-x=-1, x-z=-1".
But, finally, x=2022/3 and z=2025/3 are solutions in this video. (As for the solutions, 2022/3=674, z=2025/3=675. Therefore, they can be one of the solutions.)
According to this video's final answer, it looks like "any real number can be solutions". [ The instructor does not notice "x and z of the case 2 are integer" ・・ ?? ]
But, how to solve is treating as "x, y, z: integers". A little contradiction.
Therefore, I guess the problem condition requires "x, y, z: integers". [And the answer can be (x, y, z) = (2024, 0, 2023), (674, 2, 675) . ]
<<< If x, y, and z are real numbers, there are infinite solutions. >>>

[PhabGuy]

The issue with the method occurs when the presenter factors the "1" on the right side of the equation into (1)(1) and (-1)(-1). An unstated simplifying assumption is being made there. Of course, the right sides could be factored in an infinite number of ways, e.g. (2)(1/2), etc. yielding an infinite number of solutions.

[lmdixieentertainment]

Super Exploration Sir and
For z equal to 2025/3 is exactly 675 and 2022/3 equal to 674

[ksubrad]

I have to agree with the infinite solutions. Two equations, three unknowns. There must be additional information to solve singular values.

[reinamaeda]

The number 2025 was divisible by three and the answer was 675.
Therefore, as a whole it turned out, x=674, y=2, z=675

[eugeniodiazbarriga]

2022/3 is equal to 674, 2025/3 is equal to 675. Good exercice

[alster]

I have seen this problem from before and I knew the same principle applies.

[learnpersonally]

Actually there should be condition that x, y, z are integers,

[shadmanhasan]

Scenario 1:
z = 2023 - xy
Scenario 2:
z = (2024-x)/y
Let z=z (use desmos)

[jayadityagupta]

this is a wrong question - there is no restriction that x, y and z are integers!

[ilyashick]

X, Y, And Z is is three, but system is two rows. In this case no real solution. it is infinite numbers. maybe to better say interger only including 0 as for clarification.

[FrogworfKnight]

I am sorry, but there are infinitely more solutions than the ones given. For instance, x=0, y=2024/2023, and z=2023 is also a solution.

[kennethhannan]

Didn't someone say "quickly"?