calculate mean of two variables given two regression equations

Question

Given these 2 regression equations how do I compute mean and find $r_{XY}$.

$X=-0.4Y+6.4$

$Y=-0.6X+4.6$

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when I rearranged the equations, I solved for $X$ and $Y$ hence $X=6$, $Y=1$

How do I get mean and $r_{XY}$ using the the two values.

Answer 1

Examine the plots of the two lines:

and think about the meanings of perfect positive and negative correlation and what the values of $r_{XY}$ are for those two situations.