Regression Equation:
The given regression equation is 2y_x = 50 and 3y_2x = 10.

Finding the Mean of x and y:
To find the mean of x and y variables, we need to solve the regression equation.

Let's solve the first equation, 2y_x = 50, for y_x:
Dividing both sides of the equation by 2, we get:
y_x = 50/2 = 25

Now, let's solve the second equation, 3y_2x = 10, for y_2x:
Dividing both sides of the equation by 3, we get:
y_2x = 10/3 = 3.33

The mean of x is not given in the regression equation, so we cannot determine the mean of x from the given information.

Therefore, the mean of x is unknown, but the mean of y can be determined from the first equation, which is y_x = 25.

Finding the Coefficient of Correlation:
To find the coefficient of correlation between the x and y variables, we need more information than just the regression equation. The coefficient of correlation measures the strength and direction of the linear relationship between the variables.

However, from the given regression equation, we can make a few observations:
1. The regression equation has a positive slope, indicating a positive linear relationship between x and y.
2. The value of y_x is 25, which suggests that when x is 1 unit, y is 25 units.

Without any additional information, it is not possible to determine the exact coefficient of correlation between x and y. The coefficient of correlation can only be determined with the help of a data set that contains paired values of x and y.

Summary:
- The mean of x cannot be determined from the given regression equation.
- The mean of y is 25, as given by the first equation.
- The coefficient of correlation between x and y cannot be determined without additional information.