# 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.

×