x+y+z=5;2x-y+z=9;x-2y+3z=16 eching

$$x + y + z = 5 ; 2 x - y + z = 9 ; x - 2 y + 3 z = 16$$

x, y, z uchun yechish

$$x=2$$

$$y=-1$$

$$z=4$$

Almashtirish orqali qisqa qadamlar

x uchun x+y+z=5 ni hisoblang.

$$x=-y-z+5$$

Ikkinchi va uchinchi tenglamada x uchun -y-z+5 ni almashtiring.

$$2\left(-y-z+5\right)-y+z=9 -y-z+5-2y+3z=16$$

y va z uchun mos ravishda ushbu tenglamalarni yeching.

$$y=\frac{1}{3}-\frac{1}{3}z z=\frac{3}{2}y+\frac{11}{2}$$

z=\frac{3}{2}y+\frac{11}{2} tenglamasida y uchun \frac{1}{3}-\frac{1}{3}z ni almashtiring.

$$z=\frac{3}{2}\left(\frac{1}{3}-\frac{1}{3}z\right)+\frac{11}{2}$$

z uchun z=\frac{3}{2}\left(\frac{1}{3}-\frac{1}{3}z\right)+\frac{11}{2} ni hisoblang.

$$z=4$$

y=\frac{1}{3}-\frac{1}{3}z tenglamasida z uchun 4 ni almashtiring.

$$y=\frac{1}{3}-\frac{1}{3}\times 4$$

y ni y=\frac{1}{3}-\frac{1}{3}\times 4 orqali hisoblang.

$$y=-1$$

x=-y-z+5 tenglamasida y uchun -1 va z uchun 4 ni almashtiring.

$$x=-\left(-1\right)-4+5$$

x ni x=-\left(-1\right)-4+5 orqali hisoblang.

$$x=2$$

Tizim hal qilindi.

$$x=2 y=-1 z=4$$