solve numerically a system of nonlinear equations

Hello guys. I am new to matlab.

Currently i am having a system of two nonlinear equations to solve .I have seen that fsolve can solve nonlinear equations ,but my problem is that i dont possess optimization toolbox ,which is needed to use this function.

The system of nonlinear equations is below :

(1) : x1^2*(9.0214+x2*71.185)-67.7=0

(2) : 1/sqrt(x2)+2*log(0.0001886+0.000003513/(x1*sqrt(x2)))=0 (log base 10 )

So i ended up preferring a numerical approach.I have seen codes that solves numerically ,single equation but not for a system of equations.Can anyone help me find a solution for the above system?

Thanks

Answer 1

[Matt J]

F2=@(z) z+2*log10(0.0001886+0.000003513*z);
 
[z,Fsol]=fzero(F2,1)

z = 7.3376

Fsol = 8.8818e-16

x2=1./z.^2

x2 = 0.0186

x1=sqrt(67.7/(9.0214+x2*71.185)) % -x1 is also a solution

x1 = 2.5583

%%%Check
x1^2*(9.0214+x2*71.185)-67.7

ans = 0

1/sqrt(x2)+2*log10(0.0001886+0.000003513/sqrt(x2))

ans = 8.8818e-16

[Bill Kyriakidis]

I am sorry ,i didnt write down the second equation right . The proper system is :

(1) : x1^2*(9.0214+x2*71.185)-67.7=0

(2) : 1/sqrt(x2)+2*log(0.0001886+0.000003513/(x1*sqrt(x2)))=0 (log base 10 )

Thanks for the time spent again.