Question

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

Answer 1

$\left \{ {{2x+y=8-2x} \atop {3(x-y)-2y=29}} \right. \\ \left \{ {{4x+y=8} \atop {3x-5y=29}} \right.$
Inmultim cu 5 prima ecuatie.
$\left \{ {{20x+5y=40} \atop {3x-5y=29}} \right.$
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
$\left \{ {{2x-5y=11} \atop {3(x-y)-2x=11}} \right. \\ \left \{ {{2x-5y=11} \atop {x-3y=11}} \right.$
Se inmulteste a doua ecuatie cu -2
$\left \{ {{2x-5y=11} \atop {-2x+6y=-22}} \right.$
Adunand ecuatiile obtinem y=-11
Inlocuim y apoi in prima ecuatie
2x-5*(-11)=11, 2x+55=11, 2x=-44, x=-22