Question

la un concurs de matematica se acorda 5 puncte pentru o problema rezolvata corect si se scad 2 puncte pentru o problema rezolvata gresit . Alexandru a trimis 20 probleme rezolvate corect si a primit 72 de puncte . Cate probleme a rezolvat bine si cate a gresit ?
va rog ajuatima prin aflari !!!!!! am mare nevoie !!

Answer 1

$Notam\ probleme\ rezolvate\ corect\ cu\ x,\ iar\ pe\ cele\ gresite\ cu\ y.$
$\left \{ {{x+y=20} \atop {5*x-2*y=72}} \right. \Leftrightarrow \left \{ {{x=20-y} \atop {5(20-y)+2y=72}} \right. \Leftrightarrow \left \{ {{x=20-y} \atop {100-5y-2y=72}} \right.$

[tex]\Leftrightarrow \left \{ {{x=20-y} \atop {-7y=72-100}} \right. \Leftrightarrow \left \{ {{x=20-y} \atop {-7y=-28}} \right. \Leftrightarrow \left \{ {{x=20-y} \atop {y= \frac{-28}{-7} }} \right. [/tex]

$\Leftrightarrow \left \{ {{x=20-y} \atop {y=4}} \right. \Leftrightarrow \left \{ {{x=20-4} \atop {y=4}} \right. \Leftrightarrow \left \{ {{x=16} \atop {y=4}} \right.$