Solving a System of Equations

I am experiencing difficulties in solving the following system of equations: Υ=Χ+Α-Β*e^(-Χ/6), Υ= -10log[10^(1.76)-10^(-X/10)], where A and B are parameters defined by the user (i.e A=5, B=4). Any help could be useful. Thanks in advance!

Answer 1

[Walter Roberson]

You will need to solve this numerically. Subtract one from the other, numerically solve for a 0. Along the way you will need to decide if you are wanting natural logs or log10 .

Caution: this is pretty sensitive numerically, especially near X = -17.6

[Konstantinos]

************************************************************************

clc;

clear all;

fprintf('This program solves the system of equations which have the following form:\nY=X+A-Be^(-X/6)\nY=-10*log[10^(1.76)-10^(-X/10)]\n')

syms OBO IBO

[IBO1,OBO1]=solve('OBO=IBO+6-6*exp(IBO/6)','10^(-IBO/10)+10^(-OBO/10)=10^1.76') ********************************************************************** this peace of code works and gives me the necessary results because I set A=6 , B=6. The problem appears when I want the user to set A and B. To achieve this i use the following lines: ************************************************************************

clc;

clear all;

fprintf('This program solves the system of equations which have the following form:\nY=X+A-Be^(-X/6)\nY=-10*log[10^(1.76)-10^(-X/10)]\n')

syms OBO IBO

syms A B

A=input('Enter the value of the variable A: ');

B=input('Enter the value of the variable B: ');

[IBO1,OBO1]=solve('OBO=IBO+A-B*exp(IBO/6)','10^(-IBO/10)+10^(-OBO/10)=10^1.76') ***********************************************************************************

[Walter Roberson]

eqn1 = sym('OBO=IBO+A-B*exp(IBO/6)');
eqn2 = sym('10^(-IBO/10)+10^(-OBO/10)=10^1.76');
sA = sym('A');
sB = sym('B');
seqn1 = subs(eqn1, {sA, sB}, {A, B});
seqn2 = subs(eqn2, {sA, sB}, {A, B});
solve(seqn1, seqn2)