Stagnation points in 2D velocity field

A stagnation point is a point where the velocity is zero, i.e. both $u = 0$ and $v = 0$ at the same time.

Given: $u = 1 + 2.5x + y$, $v = -0.5 - 3x - 2.5y$.

Set both components equal to zero:

$$\begin{aligned} 1 + 2.5x + y &= 0 \quad (1)\\ -0.5 - 3x - 2.5y &= 0 \quad (2) \end{aligned}$$

From (1): $y = -1 - 2.5x$. Substituting in (2):

$$\begin{aligned} -0.5 - 3x - 2.5(-1 - 2.5x) &= 0\\ -0.5 - 3x + 2.5 + 6.25x &= 0\\ 2 + 3.25x &= 0\\ x &= -0.6154\ \text{m} \end{aligned}$$ $$y = -1 - 2.5(-0.6154) = 0.5385\ \text{m}$$

Check: $u = 1 - 1.5385 + 0.5385 = 0$ and $v = -0.5 + 1.8462 - 1.3462 = 0$.

Answer: yes, there is one stagnation point, at $(x, y) = (-0.615\ \text{m},\ 0.538\ \text{m})$.