Question

Realizati un algoritm pentru rezolvarea unui sistem de 2 ecuatii cu 2 necunoscute. (preudocod)

Answer 1

Algoritmul va rezolva urmatorul sistem:

[tex]\left\{\begin{array}{ll} a_1x+b_1y+c_1=0\\\\ a_2x+b_2y+c_2=0\rightarrow \boxed{y=\frac{-a_2x-c_2}{b_2}} \end{array}\right\\\\\\ a_1x+b_1(\frac{-a_2x-c_2}{b_2})+c_1=0\\\\ a_1x-\frac{a_2b_1}{b_2}x-\frac{b_1c_2}{b_2}+c_1=0\\\\ x(\frac{a_1b_2-a_2b_1}{b_2})=\frac{b_1c_2-b_2c_1}{b_2}\\\\ \boxed{x=\frac{b_1c_2-b_2c_1}{a_1b_2-a_2b_1}} [/tex]

Il vom calcula mai intai pe x, apoi il vom calcula pe y in functie de x.

Pseudocodul:

inceput

real a1, b1, c1, a2, b2, c2, x, y

citeste a1, b1, c1, a2, b2, c2

x <- (b1 * c2 - b2 * c1) / (a1 * b2 - a2 * b1)
y <- (-a2 * x - c2) / b2

scrie x, y

sfarsit