Question

rezolvati in RXR prin metoda utilizari necunoscutelor auxiliare sistemul de ecuati 3supra x-1-5supra y-1=-3 si 2 supra x-1 -1supra 2(y-1)=1

Answer 1

[tex] \left \{ {{\frac{3}{x-1}-\frac{5}{y-1}=-3} \atop {\frac{2}{x-1}-\frac{1}{2(y-1)}=1}} \right.\\ Notam:\frac{1}{x-1}=a\ si\ \frac{1}{y-1}=b.Astfel\ sistemul\ va\ deveni:\\ \left \{ {{3a-5b=-3} \atop {2a-\frac{b}{2}=1}} \right. \Leftrightarrow \left \{ {{3a-5b=-3} \atop {4a-b=2}} \right. \\ \text{Sistemul acesta nu e greu de rezolvat,asa ca te voi lasa pe tine sa-l}\\ \text{rezolvi.Daca il rezolvi corect,solutiile vor fi a=}\frac{13}{17} \text{ si b=}\frac{18}{17}\\ Inlocuim:\\ [/tex]
[tex]\frac{1}{x-1}=\frac{13}{17}\\ 13x-13=17\\ 13x=30\Rightarrow \boxed{x=\frac{30}{13}}\\ \frac{1}{y-1}=\frac{18}{17}\\ 18y-18=17\\ 18y=35\Rightarrow \boxed{y=\frac{35}{18}}\\ [/tex]