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un fermier creste porumbei si purcei in total sint 51 de capete si 132 de picioare aflati citi porumbei si  citi purcei are fermierul rezolva problema prin ecuatie


Răspuns :

x-nr porumbei
y-nr purcei
 [tex] \left \{ {{x+y=51|*(-2)} \atop {2x+4y=132}} \right. [/tex]
[tex] \left \{ {{-2x-2y=-102} \atop {2x+4y=132}} \right. [/tex]
[tex]2y=30
 y=15( 15 purcei)[/tex]
[tex] [tex] \left \{ {{x+y=51|*(-4)} \atop {2x+4y=132}} \right. [/tex][/tex]
[tex] \left \{ {{-4x-4y=-204} \atop {2x+4y=132}} \right. [/tex]
-2x=-72
x=36 ( 36 porumbei)

verificare:
36+15=51
2*36+4*15=72+60=132

raspuns: 15 purcei si 36 porumbei