Solve a system of non-linear equations in Python (scipy.optimize.fsolve)

[drudox]

I'm trying to solve this system of non linear equations using scipy.optimize.fsolve , I took this from an example in one other post [here][1]

my system of equation is the follow :

    for i in range(len(self.time)-1):
            
                def equations(variable):
                    k1,k2 = variable 
                    f1 = -k1 + self.f(self.time[i]+ (0.5+np.sqrt(3)/6)* self.dt , self.u[i]+0.25*self.dt* k1+ (0.25+ np.sqrt(3)/6)*self.dt*k2) 
                    f2 = -k2 + self.f(self.time[i]+ (0.5-np.sqrt(3)/6)* self.dt , self.u[i]+(0.25-np.sqrt(3)/6)*self.dt *k1 + 0.25*self.dt* k2)
                    return (f1,f2)
                            
                    
                k1,k2 = fsolve(equations,(5,5))

when I run the code I got :

    TypeError: fsolve: there is a mismatch between the input and output shape of the 'func' argument 'equations'.Shape should be (2,) but it is (2, 1).

I don't know why this mismatch and how to fix it ..
I tried :

 for i in range(len(self.time)-1):
                ui = self.u[i]
                ti = self.time[i]
    
                def equations(variable):
                    k1,k2 = variable 
                    f1 = -k1 + self.f(ti+ (0.5+np.sqrt(3)/6)* self.dt , ui+0.25*self.dt* k1+ (0.25+ np.sqrt(3)/6)*self.dt*k2) 
                    f2 = -k2 + self.f(ti+ (0.5-np.sqrt(3)/6)* self.dt , ui+(0.25-np.sqrt(3)/6)*self.dt *k1 + 0.25*self.dt* k2)
                    return (f1,f2)
                            
                    
                k1,k2 = fsolve(equations,(1,1))

how can I fix this mismatch ?