$$u_x + v_y = 0$$ $$v_x - v_y = 0$$ $$v_y - u_x = 0$$
We are instructed to solve the following system of first order equations. I have no idea where to begin. I have tried putting this into a matrix with the equations in one multiplied by one with the derivatives to equal a matrix of 0s. I have tried to find characteristic equations where the solutions will be constant and only have come up with <1,-1> for the gradient of v. I am not sure if I should simply try to integrate, but I'm almost positive this would not be effective. Any tips pushing me in the right direction would be welcome.
Partial Differential Equations course