Question

Tìm x, y, z:

\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4};2x+3y-z=50\)

Answer 1

Ta có:\(\frac{x-1}{2}=\frac{2\left(x-1\right)}{2.2}=\frac{2x-2}{4}\); \(\frac{y-2}{3}=\frac{3.\left(y-2\right)}{3.3}=\frac{3y-6}{9}\)

=> \(\frac{2x-2}{4}=\frac{3y-6}{6}=\frac{z-3}{4}\)\(=\frac{2x-2+3y-6-\left(z-3\right)}{4+9-4}=\frac{2x+3y-z-2-6+3}{9}\)

= \(\frac{50-5}{9}=45=5\)

=> \(\frac{x-1}{2}=5\Rightarrow x-1=5.2=10\Rightarrow x=11\)

=> \(\frac{y-2}{3}=5\Rightarrow y-2=5.3=15\Rightarrow y=17\)

=> \(\frac{z-3}{4}=5\Rightarrow z-3=5.4=20\Rightarrow z=23\)

Vậy x=11; y=17 và z=23