The image shows a vector field plot with arrows pointing towards the origin (0,0). The question asks for the equilibrium point of this system.

An equilibrium point in a dynamical system occurs where the velocity (or change) is zero, meaning no movement is indicated by the vector field at that point. From the vector field in the image, we can see that all arrows are pointing towards the origin, suggesting that (0,0) is the equilibrium point.

Thus, the equilibrium point of the system is:

$x = 0, \quad y = 0$

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to expand your understanding:

1. What are the different types of equilibrium points (e.g., stable, unstable, saddle)?
2. How can you determine the stability of an equilibrium point by looking at a vector field?
3. What are phase portraits, and how are they related to equilibrium points?
4. What are the mathematical conditions for finding equilibrium points in a system of differential equations?
5. How can eigenvalues help in classifying equilibrium points?

Tip: Equilibrium points can be stable (attracting), unstable (repelling), or saddle points, depending on the behavior of the vectors around them. Understanding the direction of the arrows helps in classifying these points.