Question

\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}và2x+3y-z=50\)

Answer 1

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

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

Âp dụng tính chất dãy tỉ số bằng nhau, ta có:

\(\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{z-3}{4}=\frac{2x-2+3y-6-z+3}{4+9-4}=\frac{45}{9}=5\)

=> x - 1 = 5.2 = 10 => x = 11

     y - 2 = 5.3 = 15 => y = 17

     z - 3 = 5.4 = 20 => z = 23

Answer 2

\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2\left(x-1\right)+3\left(y-2\right)-\left(z-3\right)}{2.2+3.3-4}=\frac{2x+3y-z-5}{9}=\frac{45}{9}=5\)

x-1 =2.5 => x =11

y-2 =3.5 => y =17

z-3 =4.5 => z =23