Discussion

If the two regression lines are

x + 2y = 5 and
2x + 3y = 8

then the means of x and y are :

Answer: C

The means are x = 1, y = 2.

Both regression lines pass through the point of means, so solve them together.

\[ \begin{aligned} x &= 5 - 2y \\ 2(5 - 2y) + 3y &= 8 \\ 10 - y &= 8 \Rightarrow y = 2 \\ x &= 5 - 4 = 1 \end{aligned} \]

Check: 1 + 2(2) = 5 and 2(1) + 3(2) = 8. The pair 2, 1 reverses the two means, and -3, 4 and 2, 4 do not satisfy both equations.

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