Question

Tìm x,y,zbiết: 3(x-1)=2(y-2),4(y-2)=3(z-3) và 2x+3y-z=50

Answer 1

Lời giải:

$3(x-1)=2(y-2); 4(y-2)=3(z-3)$

$\Rightarrow \frac{x-1}{2}=\frac{y-2}{3}; \frac{y-2}{3}=\frac{z-3}{4}$

$\Rightarrow \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$

Áp dụng TCDTSBN:

$\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$

$=\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{z-3}{4}$

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

$=\frac{2x+3y-z-5}{9}=\frac{50-5}{9}=5$

$\Rightarrow x-1=10; y-2=15; z-3=20$

$\Rightarrow x=11; y=17; z=23$