The teacher is wrong!

Algebra Level 3

John was given a math question.

Find a solution to \(a+bcd=b+acd=c+abd=d+abc=2\)

He solves it as follows:

Step 1: Rearrange into: \(bcd-acd=b-a\)

Step 2: Factorise into: \(cd(b-a)=b-a\)

Step 3: Divide: \(cd=1\)

Step 4: Apply to each and every equation: \(ab=ac=ad=bc=bd=cd=1\)

Step 5: Compare to get \(a=b=c=d=1\) as one of the solution.

However, his teacher marked him wrong!

What went wrong?


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