Explanation:

The regression lines of the given equations are:

- x + y = 1
- x - y = 1

Finding Mean Values of x and y:

To find the mean values of x and y, we need to calculate the sum of all x-values and y-values and divide them by the total number of observations.

Let's assume that we have n observations for x and y.

- Sum of all x-values = Σx
- Sum of all y-values = Σy

The total number of observations will be the same for both x and y, so we can write:

- Total number of observations = n

Then, the mean values of x and y can be calculated using the following formulas:

- Mean value of x = Σx / n
- Mean value of y = Σy / n

Solving for Mean Values:

Let's solve the given equations to find the values of x and y.

- x + y = 1
- x - y = 1

Adding both equations, we get:

- 2x = 2
- x = 1

Substituting the value of x in any of the equations, we get:

- 1 + y = 1
- y = 0

Therefore, the mean value of x is 1 and the mean value of y is 0.

Conclusion:

The mean value of x is 1 and the mean value of y is 0 for the given regression lines.