Given,

x + 6y = 6

3 x + 2 y =10

To find : -

(i) sample means $\overline x\ and\ \overline y$ = ?

(ii) Coefficient of correlation between x and y = ?

(i) Since the given equations are :-

x + 6y = 6 ..........(a)

3 x + 2 y =10 ..........(b)

Let's multiply equation (a) by 3 to cancel x from equation (b).

So, Now we have -

3x + 18y = 18

3x + 2y = 10

Now subtracting these two equations we get,

$\implies (3x + 18y) - (3x + 2y) = 18 - 10$

$\implies (16 y) = 8 $

$\implies y = \frac{1}{2}$

Now, Putting the value of y in equation (b) we get,

$\implies 3x + 2\frac{1}{2} = 10$

$\implies x = 3$

(ii) If the line $x + 6y = 6$ is the line of regression of y on x, then of regression of y on x, then

by $=-x + 6 $ i.e $y = -1/6x + 1 \space\space byx = -1$

If the line $3x + 2y = 10$ is the line of regression of x on y then

$$3x = -2y + 10\ i.e\ x = -2y/3 + 10/3$$

$Bxy = -2/3\\ r=\sqrt{byx\times bxy}=\sqrt{\dfrac {-1}6\times \dfrac {-2}3}=\sqrt{\dfrac 19}=\dfrac 13 $

Since byx and bxy are negative.

X is greater.

$$\therefore x=\dfrac {-1}3$$