{lll}{1}&{2}&{3}{4}&{5}&{6}{7}&{8}&{5}{l}{x}{y}{z}={l}{5}{10}{15} eching

$$\left( \begin{array} { l l l } { 1 } & { 2 } & { 3 } \\ { 4 } & { 5 } & { 6 } \\ { 7 } & { 8 } & { 5 } \end{array} \right) \left( \begin{array} { l } { x } \\ { y } \\ { z } \end{array} \right) = \left( \begin{array} { l } { 5 } \\ { 10 } \\ { 15 } \end{array} \right)$$

x, y, z uchun yechish

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1,666666667$$

$$y = \frac{10}{3} = 3\frac{1}{3} \approx 3,333333333$$

$$z=0$$

Almashtirish orqali qisqa qadamlar

x uchun x+2y+3z=5 ni hisoblang.

$$x=-2y-3z+5$$

Ikkinchi va uchinchi tenglamada x uchun -2y-3z+5 ni almashtiring.

$$4\left(-2y-3z+5\right)+5y+6z=10 7\left(-2y-3z+5\right)+8y+5z=15$$

y va z uchun mos ravishda ushbu tenglamalarni yeching.

$$y=\frac{10}{3}-2z z=\frac{5}{4}-\frac{3}{8}y$$

z=\frac{5}{4}-\frac{3}{8}y tenglamasida y uchun \frac{10}{3}-2z ni almashtiring.

$$z=\frac{5}{4}-\frac{3}{8}\left(\frac{10}{3}-2z\right)$$

z uchun z=\frac{5}{4}-\frac{3}{8}\left(\frac{10}{3}-2z\right) ni hisoblang.

$$z=0$$

y=\frac{10}{3}-2z tenglamasida z uchun 0 ni almashtiring.

$$y=\frac{10}{3}-2\times 0$$

y ni y=\frac{10}{3}-2\times 0 orqali hisoblang.

$$y=\frac{10}{3}$$

x=-2y-3z+5 tenglamasida y uchun \frac{10}{3} va z uchun 0 ni almashtiring.

$$x=-2\times \frac{10}{3}-3\times 0+5$$

x ni x=-2\times \frac{10}{3}-3\times 0+5 orqali hisoblang.

$$x=-\frac{5}{3}$$

Tizim hal qilindi.

$$x=-\frac{5}{3} y=\frac{10}{3} z=0$$