Calculating the Variance of x given the Regression Equations
In order to find the variance of x, we need to first solve the system of equations given:
2x + 3y = 20
3x - 5y = 10

Finding the Values of x and y
We can solve the system of equations by substitution or elimination method to find the values of x and y. Once we have the values of x and y, we can calculate the variance of x.

Calculating the Variance of x
Once we have the values of x, we can calculate the variance of x using the formula:
Variance of x = Σ(x - μx)² / n
where μx is the mean of x, n is the number of observations, and Σ represents the sum of the values.

Explanation of the Solution
By solving the system of equations and finding the values of x and y, we can then calculate the variance of x using the formula mentioned above. The variance of x gives us an idea of how much the values of x deviate from the mean. In this case, since the variance of y is given as 5, we can use the regression equations to determine the variance of x.
By following these steps and calculations, we can find the variance of x based on the given regression equations.