Solving system of 2 non linear equations

Good evening everyone,

I must solve this system of two non linear equations:

0.00014/(3.85E-05*cos((x-y)*0.006))-(0.196*0.026*tan((x-y)*0.0062)*tanh(x*0.026))/0.006+0.196-0.00014/3.85E-05=2.0051

2.005+(y-300)*((y-300)*6.31E-05/2-((0.196*3.85E-05-0.00014)*sin((x-y)*0.0062))/0.0062+0.196*0.026*cos((x-y)*0.0062)*tanh(x*0.026))=2.9905

What is the best approach to obtain a solution? I know that x and y should be in the range of (0,300), and x is lower than y.

Thanks in advance

[Alex Sha]

if x and y are limited in the range of [0,300], the result will be:

x: 106.852495887777
y: 221.905657509353

Answer 1

[Paul]

syms x y real
eq1 = 0.00014/(3.85E-05*cos((x-y)*0.006))-(0.196*0.026*tan((x-y)*0.0062)*tanh(x*0.026))/0.006+0.196-0.00014/3.85E-05 == 2.0051; 
eq2 = 2.005+(y-300)*((y-300)*6.31E-05/2-((0.196*3.85E-05-0.00014)*sin((x-y)*0.0062))/0.0062+0.196*0.026*cos((x-y)*0.0062)*tanh(x*0.026)) == 2.9905;
sol = vpasolve([eq1,eq2],[x y],[0 300;0 300])

sol = struct with fields:
    x: 106.85249588777741184146319523654
    y: 221.90565750935273789837170961006

% verify
vpa(subs(lhs([eq1;eq2]),sol)-rhs([eq1;eq2]))

ans = 

[Matteo Canestri]

Thank you very much.

Works like a charm.