Question

Tìm x;y;z biết:

\(\frac{9x-13}{16}=\frac{7y-11}{19}=\frac{z-5}{3}\)và 5x-7y+3z=9

Answer 1

\(\frac{9x-13}{16}=\frac{7y-11}{19}=\frac{z-5}{3}=k\)

\(\frac{45x-65}{80}=\frac{63y-99}{171}=\frac{27z-45}{27}=k\)

Suy ra

\(k=\frac{45x-65-63y+99+27x-45}{80-171+27}\)

\(k=\frac{9\left(5x-7y+3z\right)-11}{-64}=\frac{81-11}{-64}=-\frac{35}{32}\)

\(\frac{9x-13}{16}=-\frac{35}{32}\Rightarrow x=-16\)

\(\frac{7y-11}{19}=-\frac{35}{32}\Rightarrow y=-\frac{313}{224}\)

\(\frac{z-5}{3}=-\frac{35}{32}\Rightarrow z=\frac{55}{32}\)