Problem 11

Contents

(a) Find solutions of nonlinear system using solve

Matlab finds two solutions for (x,y): The point (1,0) and the point (5/3,-4/3).

syms x y real               % declare x, y as real symbolic variables
f1 = x^2 - y^2 - 1
f2 = 2*x + y - 2
[xs,ys] = solve(f1,f2,x,y)  % find all x,y such that f1=0 and f2=0
                            % 1st solution is xs(1), ys(1)
                            % 2nd solution is xs(2), ys(2)

f1 =
x^2-y^2-1
f2 =
2*x+y-2
xs =
   1
 5/3
ys =
    0
 -4/3

(b) Plot two curves and solution points

We plot the points in the rectangle -3<x<3, -3<y<3 where f1=0 and f2=0:

ezplot(f1,[-3 3 -3 3]); hold on  % f1=0 gives hyperbola
ezplot(f2,[-3 3 -3 3]);          % f2=0 gives straight line
plot(double(xs),double(ys),'ro'); hold off
                           % mark two intersection points with read circles

Published with MATLAB® 7.0.1