Finalement, I found the solution. I post the script in case anyoone is interested in.
clc, clear all close all
set(0,'defaultTextInterpreter','latex');
% visualisation des plans
% premier plan
x1 = 0:0.5:10; x2 = 0:0.5:3;
[X Y] = meshgrid(x1,x2);
Z = 3-Y-(3/10)*X;
H1 = surf(X,Y,Z);
set(H1,'facecolor', 'r','FaceAlpha',0.3, 'EdgeColor' ,'none')
hold on
% deuxième plan
x1 = 0:0.5:2; x2 = 0:0.5:20;
[X Y] = meshgrid(x1,x2);
Z = 2-X-(1/10)*Y;
H2 = surf(X,Y,Z);
set(H2,'facecolor', 'b','FaceAlpha',0.3, 'EdgeColor','none')
% troisième plan
x1 = 0:0.5:5; x2 = 0:0.5:10;
[X Y] = meshgrid(x1,x2);
Z = 0.5*(1-(1/5)*X-(1/10)*Y);
H3 = surf(X,Y,Z);
set(H3,'facecolor', 'g','FaceAlpha',0.3, 'EdgeColor' ,'none')
% point d'intersection
% point d'intersection
A = [1/10, 1/3, 1/3; 1/2, 1/20, 1/2; 1/5, 1/10, 1/0.5]; C = [1, 1, 1]';
X_sol = A\C;
plot3(X_sol(1), X_sol(2), X_sol(3), 'k.', 'MarkerSize', 30)
plot3(X_sol(1), X_sol(2), X_sol(3), 'k.', 'MarkerSize', 30)
% lines of intersections
% line of intersection of first two planes
% calculate intersection in plane z = 0
A1 = [ 1/10 1/3 ; 1/2 1/20 ];
B1 = [ 1; 1 ];
X1 = A1\B1;
P1 = [ X1; 0 ];
% calculate intersection in plane x = 0
A2 = [ 1/3 1/3 ; 1/20 1/2 ];
B2 = [ 1; 1 ];
X2 = A2\B2;
P2 = [ 0; X2 ];
P1P2 = [P1, P2];
line(P1P2(1,:), P1P2(2,:), P1P2(3,:), 'Color',...
'black', 'linewidth',1.5); view(3)
% line of interesection of first and third plane
% calculate intersection in plane z = 0
A1 = [ 1/10 1/3 ; 1/5 1/10 ];
B1 = [ 1; 1 ];
X1 = A1\B1;
P1 = [ X1; 0 ];
% calculate intersection in plane x = 0
A2 = [ 1/3 1/3 ; 1/10 1/0.5 ];
B2 = [ 1; 1 ];
X2 = A2\B2;
P2 = [ 0; X2 ];
P1P2 = [P1, P2];
line(P1P2(1,:), P1P2(2,:), P1P2(3,:), 'Color','black',...
'linewidth',1.5); view(3)
% line of interesection of second and third plane
% calculate intersection in plane z = 0
A1 = [ 1/2 1/20 ; 1/5 1/10 ];
B1 = [ 1; 1 ];
X1 = A1\B1;
P1 = [ X1; 0 ];
% calculate intersection in plane y = 0
A2 = [1/2 1/2; 1/5 1/0.5];
B2 = [ 1; 1 ];
X2 = A2\B2;
P2 = [X2(1); 0; X2(2)];
P1P2 = [P1, P2];
line(P1P2(1,:), P1P2(2,:), P1P2(3,:), 'Color',...
'black', 'linewidth',1.5); view(3)
% plot settings and labeling
axis square, grid on, grid minor, box on
xlabel('$x_1$'), ylabel('$x_2$'), zlabel('$x_3$')
set(gca,'FontSize',16)
xlim([0 10]) , ylim([0 20]), zlim([0 3])
set(gca, 'Xdir', 'reverse', 'YDir', 'reverse')
title({'Trois plans et leurs intersections',...
'$\frac{1}{10}x_1+\frac{1}{3}x_2+\frac{1}{3}x_3=1$ (red)',...
'$\frac{1}{2}x_1+\frac{1}{20}x_2+\frac{1}{2}x_3=1$ (blue)',...
'$\frac{1}{5}x_1+\frac{1}{10}x_2+\frac{1}{0.5}x_3=1$ (green)'})
hold off
set(0,'defaultTextInterpreter','none');
