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RAZLIĈITI METODI REŠAVANJA SISTEMA LINEARNIH JEDNAĈINA. DIFFERENT METHODS OF
SOLVING A SYSTEM OF LINEAR EQUATIONS

Uĉenik: DAVID AVRIĆ VIII razred OŠ "Olga Petrov "
Mentor: VESNA RAJŠIĆ profesor matematike Elektrotehniĉka škola " Nikola Tesla "

REZIME
U razliĉitim naukama postoje problemi koji se najlakše rešavaju pomoću sistema linearnih jednaĉina. U radu su
prikazane vrste sistema linearnih jednaĉina i razliĉiti metodi rešavanja. Sistemi linearnih jednaĉina koji se najviše koriste
su kvadratni sistemi, jer oni najĉešće imaju jedinstveno rešenje. Oni su najviše obradjivani u radu. Cilj istraţivanja je bio
prikazati razliĉite metode kojima se mogu rešiti sistemi linearnih jednaĉina.
U radu su prikazane sledeće metode:
A) Za rešavanje sistema linearnih jednaĉina sa dve nepoznate:
1. Metod zamene
2. Metod suprotnih koeficijenata ( Gausov metod)
3. Grafiĉki metod
4. Metod determinanti ( Kramerov metod)
B) Za rešavanje sistema linearnih jednaĉina sa sa više nepoznatih:
1. Gausov metod
2. Metod determinanti ( Kramerov metod)
U okviru Kramerove metode obradjen je pojam determinanti, Sarusovo pravilo za izraĉunavanje determinanti trećeg
reda i Laplasovo pravilo za rešavanje determinanti n-tog reda.
Kljuĉne reĉi : jednaĉina, sistem, nepoznata, koeficijent, rešenje.

SUMMARY
In different of sciences there are problems which are solved most easily with systems of linear equations. The types of
systems of linear equations and different methods of solving them are presented in the paper. Systems of linear
equations are used for the most part are square systems, because they most often have a unique solution. They are
expounded most in the paper. The aim of the study was to present the different methods with which systems of linear
equations can be solved.
The following methods are presented in the paper:
A) Solving a system of linear equations in two variables:
1. Method of substitutions
2. Method of opposite coefficients ( Gaussian method)
3. Graphical method
4. Method of determinants ( Cramer's method )
B) Solving a system of linear equations in more than two variables:
1. Gaussian method
2. Method of determinants ( Cramer's method )
Within Cramer's method the concept of detarminants, Sarrus' rule for computing the detarminants of a 3-by-3 matrix and
Laplace's rule for computing the detarminants of an
n-by-n matrix are explained.