{l}{x=y+2z}{3x-z=7}{3z-y=7} eching

$$\left\{ \begin{array} { l } { x = y + 2z } \\ { 3 x - z = 7 } \\ { 3 z - y = 7 } \end{array} \right.$$

x, y, z uchun yechish

$$x=3$$

$$y=-1$$

$$z=2$$

Almashtirish orqali qisqa qadamlar

3x-z=7 tenglamasida x uchun y+2z ni almashtiring.

$$3\left(y+2z\right)-z=7$$

y uchun ikkinchi tenglamani va z uchun uchinchi tenglamani yeching.

$$y=\frac{7}{3}-\frac{5}{3}z z=\frac{7}{3}+\frac{1}{3}y$$

z=\frac{7}{3}+\frac{1}{3}y tenglamasida y uchun \frac{7}{3}-\frac{5}{3}z ni almashtiring.

$$z=\frac{7}{3}+\frac{1}{3}\left(\frac{7}{3}-\frac{5}{3}z\right)$$

z uchun z=\frac{7}{3}+\frac{1}{3}\left(\frac{7}{3}-\frac{5}{3}z\right) ni hisoblang.

$$z=2$$

y=\frac{7}{3}-\frac{5}{3}z tenglamasida z uchun 2 ni almashtiring.

$$y=\frac{7}{3}-\frac{5}{3}\times 2$$

y ni y=\frac{7}{3}-\frac{5}{3}\times 2 orqali hisoblang.

$$y=-1$$

x=y+2z tenglamasida y uchun -1 va z uchun 2 ni almashtiring.

$$x=-1+2\times 2$$

x ni x=-1+2\times 2 orqali hisoblang.

$$x=3$$

Tizim hal qilindi.

$$x=3 y=-1 z=2$$