1.[tex] \frac{x}{y} [/tex]=[tex] \frac{4}{6} [/tex]
(schimbam mezii intre ei si obtinem)
[tex] \frac{x}{4} [/tex]=[tex] \frac{y}{6} [/tex]=t⇔[tex] \left \{ {{x=4t} \atop {y=6t}} \right. [/tex]
(t=coeficientul de proportionalitate)
ma=[tex] \frac{x+y}{2} [/tex]=-10⇒x+y=-10×2=-20
(acum ca am aflat suma numerelor inlocuim x+y cu numerele de la raport adica 4t si 6t)
x+y=-20
4t+6t=-20
10t=-20
t=-2⇒x=4×(-2)=-8
y=6×(-2)=-12
2.{a,b.c}d.p{2,6,-4}⇔[tex] \frac{a}{2} [/tex]=[tex] \frac{b}{6} [/tex]=[tex] \frac{c}{-4} [/tex]=t⇒a=2t
b=6t
c=-4t
a+2c=42
2t+2×(-4t)=42
-6t=42
t=-7⇒a=-14
b=-42
c=+28
5.3x+4=16 2y-6=y
3x=16-4 2y-y=6
3x=12 y=6
x=4
5.{a,b}i.p{4,6}⇔a×4=b×6⇔[tex] \frac{a}{6} [/tex]=[tex] \frac{b}{4} [/tex]=t⇒a=6t
b=4t
a+b=15
6t+4t=15
10t=15
t=[tex] \frac{15}{10} [/tex]=[tex] \frac{3}{2} [/tex]
a=6×[tex] \frac{3}{2} [/tex]=9
b=4×[tex] \frac{3}{2} [/tex]=6
