**Solving the Equation by Equating the Coefficients**

To solve the given equation √7x - √3y = 0, we need to isolate either x or y. Let's isolate x:

Step 1: Move √3y to the other side of the equation.
√7x = √3y

Step 2: Square both sides of the equation to eliminate the square root.
(√7x)^2 = (√3y)^2
7x = 3y

Step 3: Divide both sides of the equation by 7 to solve for x.
x = 3y/7

Now, let's solve the second equation √5x √2y = 0:

Step 1: Since the product of two square roots is zero, either √5x = 0 or √2y = 0.

Case 1: √5x = 0
Squaring both sides of the equation, we get:
(√5x)^2 = 0^2
5x = 0
Dividing both sides by 5, we find:
x = 0/5
x = 0

Case 2: √2y = 0
Squaring both sides of the equation, we get:
(√2y)^2 = 0^2
2y = 0
Dividing both sides by 2, we find:
y = 0/2
y = 0

Thus, we have two possible solutions for the second equation:
Case 1: x = 0
Case 2: y = 0

**Summary**

The solution to the given system of equations is either x = 0, y = 0 or x = 3y/7, y = 0.

It has infinetly many solutions .