Systèmes d'équations
Author: Daniel Mentrard
Date: mars 2008

I

Recta  D_1

Recta D_2

Ecuación n°1: 

 a'x+b'y = c'

Ecuación n° 2 : 

 a x+b y = c

(D_1)

(D_2)

El punto I, intersección de las rectas (D_1) y (D_2),constituye
la solución gráfica del sistema de ecuaciones.

Resolver el sistema (S) formado por las dos ecuaciones, 
consiste en encontrar todos los pares de valores que son
soluciones de las dos ecuaciones a la vez.
Gráficamente consiste pues en hallar la intersección  I 
de las dos rectas (D1) y (D2).

(1)

(2)

(1)

(2)

a = -5 (slider from -50 to 50, step 0.01)
b = -5 (slider from -50 to 50, step 0.1)
c = -40 (slider from -50 to 50, step 0.1)
a' = 4 (slider from -50 to 50, step 0.1)
b' = -5 (slider from -50 to 50, step 0.1)
c' = -14 (slider from -50 to 50, step 0.1)
A = (-7, 9.5)
B = (1, 9.5)
D_1: a * x + b * y = c
D_2: a' * x + b' * y = c'
I = Intersect(D_1, D_2)
C = (14.01877493300351, -13.244314943712599)
D = (48.32054636157514, -13.244314943712599)
E = (48.11138921871799, -54.72714827704603)
F = (14.049886621315196, -55.88592490042265)
poly1, c_3, d, e, f = Polygon(C, D, E, F)
G = (-22, -14)
H = (15.084393073593077, -13.871399567099568)
J = (15.502707359307362, -25.096166233766237)
K = (-22, -25)
poly2, g, h, j, k = Polygon(G, H, J, K)
m(x) = -(a) / b * x + c / b
f1 = Function(m, -14.0, 14.0)
T3: "" + D_1
p(x) = -(a') / b' * x + c' / b'
g1 = Function(p, -14.0, 14.0)
T4: "" + D_2
L = (-14, 16)
M = Point(f)
N = Intersect(f, g)
O = Point(g)
poly3, l, m_1, n, o = Polygon(L, M, N, O)
P = Point(g1)
Q = Point(f1)
T14: "y = " + (-1.0 * a / b) + " x  + " + (c / b)
T15: "y = " + (-1.0 * a' / b') + " x  +  " + (c' / b')
T17: "I (" + (x(I)) + " ; " + (y(I)) + " )"
R = Point(poly1)
S = (22.942966325259903, 16.155993362906933)
T = (23.280201263646703, -0.2721657785071731)
i = Segment(S, T)
U = (14.656622124898536, 6.328003729920195)
V = (21.931261510099503, 6.328003729920195)
W = (23.954671140420302, 6.328003729920195)
Z = (32.00013324193396, 6.328003729920195)
A1 = (21.903647160460913, 4.0481764197695425)
B1 = (32, 4)
C1 = (24, 4)
D1 = (14.656622124898536, 4.01553558098214)
poly4, u, v, a1, d1 = Polygon(U, V, A1, D1)
poly5, w, z, b1, c1 = Polygon(W, Z, B1, C1)
T21: "" + D_1
T22: "" + D_2
E1 = (16.48176419769543, -4)
F1 = (16.48176419769543, -6)
G1 = (17.017266693606135, -3.4518094832970005)
H1 = (17.06544311337568, -6.197865410160942)
q = Segment(E1, F1)
r = Segment(E1, G1)
s = Segment(H1, F1)
I1 = (25, -4)
J1 = (33, -4)
K1 = (33, -6)
L1 = (25, -6)
poly6, i1, j1, k1, l1 = Polygon(I1, J1, K1, L1)
T12: "y =  \;  \frac{ " + (-1.0 * a) + " }{ " + b + "} \; x +  \frac{" + c + " }{" + b + "} "
T13: "y = \;  \frac{" + (-1.0 * a') + " }{" + b' + " } \; x + \frac{ " + c' + " }{" + b' + " }"