Ten is Twenty

Algebra Level 1

Here is a proof that \(10 = 20:\)

Step 1: Consider the system of equations \[2x + 4y = 20 \\ x + 2 y = 5. \] Step 2: We can rewrite the second equation as \[ x = 5 - 2y. \] Step 3: Now, plugging \(x=5 - 2y\) into the first equation, we get \[ 2(5-2y) + 4y = 20. \] Step 4: Simplifying, we have \[ 10 - 4y + 4y = 20. \] Step 5: Cancelling out the two \(4y\)'s, we get \[10 = 20.\]

Where did the proof go wrong?

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