[tex] \left \{ {{2x=-6-5y} \atop {4x+3y-9=0}} \right. -\ \textgreater \ \left \{ {{2x=-6-5y} \atop {-12-10y+3y-9=0}} \right. -\ \textgreater \ \left \{ {{2x=-6-5y} \atop {-7y-21= 0 }} \right. [/tex][tex] \left \{ {{2x+5y+6=0} \atop {4x+3y-9=0}} \right. [/tex] prima ecuatie din sistem se inmulteste cu (-2). -> [tex] \left \{ {{-4x-10y-12=0} \atop {4x+3y-9=0}} \right. [/tex] 4x si cu -4x se reduc -> adunam termenii care au ramas -> -10y+3y-9-12=0 -> -7y -21=0 -> -7y =21 | impartim la -7. -> y = -3. Acum luam prima ecuatie din sistem si inlocuim y-ul cu -3. -> 2x+5y+6 =0 -> 2x+5y = -6 -> 2x -15 = -6 -> 2x = -6 +15 -> 2x = 9 | impartim la 2 -> x = [tex] \frac{9}{2} [/tex] .. Testam si in a doua ecuatie din sistem -> 4x+3y -9 = 0 -> 4x +3y=9 -> 4x -9 = 9 -> 4x = 18 | impartim la 4 -> x = [tex] \frac{18}{4} [/tex] -> simplificam cu 2 si rezulta x = [tex] \frac{9}{2} [/tex] asta e moteda reducerii... acm urmeaza metoda substitutiei. ->[tex] \left \{ {{2x=-6-5y} \atop {4x+3y-9=0}} \right. -\ \textgreater \ \left \{ {{2x=-6-5y} \atop {-12-10y+3y-9=0}} \right. -\ \textgreater \ \left \{ {{2x=-6-5y} \atop {-7y-21=0}} \right. [/tex] -> -7y-21=0 -> -7y=21 ,impartim la -7 -> y=-3. si acum avem in sistem o varianta de a afla x-ul -> 2x=-5y-6 -> 2x = 15-6 -> 2x = 9 | impartim la 2 -> x = [tex] \frac{9}{2} [/tex]
