How to solve non linear equations with two unknowns?

Kindly help me solving these equations

eqn1 = -(49*sin(x1 + x2) - 120*cos(x1) + 20*cos(x2) + 392*sin(x1) - 10)/(30*cos(x2) + 110) =0
eqn2 = -(539*sin(x1 + x2) + 10*cos(x2) + 120*cos(x1)*cos(x2) - 392*cos(x2)*sin(x1) - 20*cos(x2)^2 + 98*sin(x1 + x2)*cos(x2))/(30*cos(x2) + 110)=0

I have tried solving them but could`t find their solutions.

Answer 1

[Star Strider]

Using fsolve and converting your assignments to anonymous functions, you can get one set of solutions:

eqn1 = @(x1,x2) -(49*sin(x1 + x2) - 120*cos(x1) + 20*cos(x2) + 392*sin(x1) - 10)/(30*cos(x2) + 110);
eqn2 = @(x1,x2) -(539*sin(x1 + x2) + 10*cos(x2) + 120*cos(x1)*cos(x2) - 392*cos(x2)*sin(x1) - 20*cos(x2)^2 + 98*sin(x1 + x2)*cos(x2))/(30*cos(x2) + 110);
eqn12 = @(xv) [eqn1(xv(1),xv(2)); eqn2(xv(1),xv(2))];

x_soln = fsolve(eqn12, [1; 1])

x_soln =
   274.4959e-003
  -274.4959e-003

Since your functions are periodic in the variables, there are an infinity of solutions. Using an initial parameter estimate of [1000,1000], the solutions are:

x_soln =
   999.3010e+000
   998.7520e+000

So choose the initial estimates close to those you want.

Answer 2

[Azzi Abdelmalek]

syms x1 x2
eqn1 = -(49*sin(x1 + x2) - 120*cos(x1) + 20*cos(x2) + 392*sin(x1) - 10)/(30*cos(x2) + 110) 
eqn2 = -(539*sin(x1 + x2) + 10*cos(x2) + 120*cos(x1)*cos(x2) - 392*cos(x2)*sin(x1) - 20*cos(x2)^2 + 98*sin(x1 + x2)*cos(x2))/(30*cos(x2) + 110)
sol=solve(eqn1,eqn2)
x1=double(sol.x1)
x2=double(sol.x2)