# If the two lines of regression are $5x+3y=55$ and $7x+y=45$ then find the correlation coefficient between $x$ and $y$

$\begin {array} {1 1} (A)\;-\sqrt{\large\frac{5}{21}} & \quad (B)\;\sqrt{\large\frac{5}{21}} \\ (C)\;\large\frac{5}{21} & \quad (D)\;None \: of \: these \end {array}$

$5x+3y=55$............(i)
$7x+y=45$............(ii)
If we regard (i) as line of regression of $y$ on $x$ and (ii) that of $x$ on $y$ then
$b_{yx} =$ Slope of (i)
$= -\large\frac{5}{3}$
$b_{xy} = \large\frac{1}{slope \: of \: (ii)}$
$= -\large\frac{1}{7}$
$r = -\sqrt{b_{yx}+b_{xy}}$
$= -\sqrt{\large\frac{5}{3} \times \large\frac{1}{7}}$
$= -\sqrt{\large\frac{5}{21}}$