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Rezolvati sistemele prin metoda reducerii
[tex] \left \{ {{2x+y=8-2x} \atop {3(x-y)-2y=29}} \right. [/tex]
[tex] \left \{ {{2x-5y=11} \atop {3(x-y)-2x=11}} \right. [/tex]


Răspuns :

[tex] \left \{ {{2x+y=8-2x} \atop {3(x-y)-2y=29}} \right. \\ \left \{ {{4x+y=8} \atop {3x-5y=29}} \right. [/tex]
Inmultim cu 5 prima ecuatie.
[tex] \left \{ {{20x+5y=40} \atop {3x-5y=29}} \right. [/tex]
Adunand ecuatiile obtinem 23x=69, x=3
Se inlocuieste x-ul cu 3 in prima ec ca e mai simpla.
4*3+y=8, 12+y=8, y=-4
 Iar la a doua
[tex] \left \{ {{2x-5y=11} \atop {3(x-y)-2x=11}} \right. \\ \left \{ {{2x-5y=11} \atop {x-3y=11}} \right. [/tex]
Se inmulteste a doua ecuatie cu -2
[tex] \left \{ {{2x-5y=11} \atop {-2x+6y=-22}} \right. [/tex]
Adunand ecuatiile obtinem y=-11
Inlocuim y apoi in prima ecuatie
2x-5*(-11)=11, 2x+55=11, 2x=-44, x=-22