Răspuns:
1. a) [tex]\left \{ {{2x+y=11} \atop {x+2y=16}} \right.[/tex] => x= 16-2y inlocuim in prima ecuatie
2*(16-2y)+y= 11 32 -4y+y=11 32-11=3y 3y=21 y=21:3 y=7
x=16-14=2 x=2 (solutie x=2, y=7)
b) [tex]\left \{ {{4x+y=25} \atop {x+4y=25}} \right.[/tex] x= 25-4y inlocuim in prima ec
4*(25-4y)+y=25 100 -16y +y=25 100-25= 15y 15y= 75 y=5
x=25-20= 5 (sol x=5, y=5)
f) [tex]\left \{ {{7x+2y=45} \atop {2x+7y=45}} \right.[/tex] | inmultim prima ec cu 7 si a doua cu 2
49x+14y=45*7 le scadem si obtinem
4x+14y=45*2 45x= 45*7-90= 315 -90
45x=225 => x= 225: 45 x= 5
2y=45-7*5=45-35=10 2y=10 => y=5
solutie (x=5, y=5)
