Proof that 2=1

Algebra Level 2

The following are my steps when I proved that \(2=1\).

Step 1. Suppose that\(:\) \(y=b\)

Step 2. Multiply both sides by \(y\)\(:\) \(y^2=yb\)

Step 3. Subtract \(b^2\) from both sides\(:\) \(y^2-b^2=yb-b^2\)

Step 4. Factor both sides\(:\) \((y-b)(y+b)=b(y-b)\)

Step 5. Divide both sides by \(y-b\)\(:\) \(y+b=b\)

Step 6. Since \(y=b\), substitute\(:\) \(b+b=b\) or \(2b=b\)

Step 7. Divide both sides by \(b\)\(:\) \(2=1\)

Is there something with my calculation? If your answer is \(no\), give your answer as \(10\). If your answer is \(yes\), input the step number which I first committed a mistake.

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