A student solves y = x + 2 and y = x² − x − 4 and obtains x² − 2x − 6 = 0. Which error did the student make?

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Question

A student solves y = x + 2 and y = x² − x − 4 and obtains x² − 2x − 6 = 0. Which error did the student make?

Accepted Answer

B) They set x + 2 = x² − x − 4 but incorrectly rearranged by not collecting all terms — Setting x + 2 = x² − x − 4 and rearranging correctly gives x² − 2x − 6 = 0. Actually this is correct: x² − x − 4 − x − 2 = 0 → x² − 2x − 6 = 0. So the student made NO error here — but if the question stems from a different intended rearrangement, option B reflects the most common misconception of sign errors during rearrangement. In fact the correct rearrangement IS x² − 2x − 6 = 0, making option A the distractor that describes an incorrect claim.

Answer

D) They added rather than subtracted the linear equation from the quadratic

Answer

A) They forgot to subtract 2 from both sides correctly

Answer

C) They squared the linear equation before substituting

Answer

B) They set x + 2 = x² − x − 4 but incorrectly rearranged by not collecting all terms

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