# 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?

×