long runtime when trying to solve a simple system

First of all, I am a newbie to matlab, so maybe I am commiting an ovbious error. All feedback is thankfully accepted.

I have coded a simple program in order to find the solutions to a system of two algebraic equations. When I start it, it can be running for an hour and it doesn't find the solution. I also find it strange because I figured it should strain my CPU, but it runs at only 10% usage.

syms x y;
[solx,soly] = solve((100*pi*(x.^2))/((((y-x)/2)+0.0022*(x.^2)-0.158*x+0.21)*pi*(x-(3^(1/2)*(-0.0006*(x.^2)+0.0569*x+0.6606)))) == 690, (7850*((y^3)-pi*((-0.0022*(x^2)+0.158*x-0.21)*(1.0498*x+5.3137)*(1.0498*x+5.3137))-(0.5*pi)*(y-x*(0.0022*(x^2)-0.158*x+0.21)))) == 10);
disp [solx,soly]

Is the code wrong? Am I missing something? I just want to find the values of x and y.

Answer 1

[Walter Roberson]

Exact solutions requires the roots of a degree 12 polynomial.

syms x y;
eqn = [(100*pi*(x.^2))/((((y-x)/2)+0.0022*(x.^2)-0.158*x+0.21)*pi*(x-(3^(1/2)*(-0.0006*(x.^2)+0.0569*x+0.6606)))) == 690, (7850*((y^3)-pi*((-0.0022*(x^2)+0.158*x-0.21)*(1.0498*x+5.3137)*(1.0498*x+5.3137))-(0.5*pi)*(y-x*(0.0022*(x^2)-0.158*x+0.21)))) == 10]

eqn = 

%
% [solx, soly] = solve(eqn)
string(eqn)

ans = 1×2 string array
    "(100*x^2)/((x - 3^(1/2)*((569*x)/10000 - (3*x^2)/5000 + 3303/5000))*(y/2 - (329*x)/500 + (11*x^2)/5000 + 21/100)) == 690"    "7850*y^3 - 3925*pi*(y - x*((11*x^2)/5000 - (79*x)/500 + 21/100)) + 7850*pi*((5249*x)/5000 + 53137/10000)^2*((11*x^2)/5000 - (79*x)/500 + 21/100) == 10"

part_y = solve(eqn(1), y)

part_y = 

eqn2 = subs(eqn(2), y, part_y)

eqn2 = 

part_x = solve(eqn2, x);
full_x = part_x

full_x = 

full_y = subs(part_y, x, full_x)

full_y = 

vpa(full_x, 16)

ans = 

vpa(full_y, 16)

ans =