frac{P_{1}V_{1}}{T_{1}}=frac{P_{2}V_{2}}{T_{2}} eching

$$\frac { P _ { 1 } V _ { 1 } } { T _ { 1 } } = \frac { P _ { 2 } V _ { 2 } } { T _ { 2 } }$$

P_1 uchun yechish (complex solution)

$$\left\{\begin{matrix}P_{1}=\frac{P_{2}T_{1}V_{2}}{T_{2}V_{1}}\text{, }&T_{2}\neq 0\text{ and }V_{1}\neq 0\text{ and }T_{1}\neq 0\\P_{1}\in \mathrm{C}\text{, }&\left(V_{2}=0\text{ or }P_{2}=0\right)\text{ and }V_{1}=0\text{ and }T_{2}\neq 0\text{ and }T_{1}\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini T_{1}T_{2} ga, T_{1},T_{2} ning eng kichik karralisiga ko‘paytiring.

$$T_{2}P_{1}V_{1}=T_{1}P_{2}V_{2}$$

Shartlarni qayta saralash.

$$P_{1}T_{2}V_{1}=P_{2}T_{1}V_{2}$$

Tenglama standart shaklda.

$$T_{2}V_{1}P_{1}=P_{2}T_{1}V_{2}$$

Ikki tarafini T_{2}V_{1} ga bo‘ling.

$$\frac{T_{2}V_{1}P_{1}}{T_{2}V_{1}}=\frac{P_{2}T_{1}V_{2}}{T_{2}V_{1}}$$

T_{2}V_{1} ga bo'lish T_{2}V_{1} ga ko'paytirishni bekor qiladi.

$$P_{1}=\frac{P_{2}T_{1}V_{2}}{T_{2}V_{1}}$$

P_2 uchun yechish (complex solution)

$$\left\{\begin{matrix}P_{2}=\frac{P_{1}T_{2}V_{1}}{T_{1}V_{2}}\text{, }&T_{1}\neq 0\text{ and }V_{2}\neq 0\text{ and }T_{2}\neq 0\\P_{2}\in \mathrm{C}\text{, }&\left(V_{1}=0\text{ or }P_{1}=0\right)\text{ and }V_{2}=0\text{ and }T_{1}\neq 0\text{ and }T_{2}\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini T_{1}T_{2} ga, T_{1},T_{2} ning eng kichik karralisiga ko‘paytiring.

$$T_{2}P_{1}V_{1}=T_{1}P_{2}V_{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$T_{1}P_{2}V_{2}=T_{2}P_{1}V_{1}$$

Tenglama standart shaklda.

$$T_{1}V_{2}P_{2}=P_{1}T_{2}V_{1}$$

Ikki tarafini T_{1}V_{2} ga bo‘ling.

$$\frac{T_{1}V_{2}P_{2}}{T_{1}V_{2}}=\frac{P_{1}T_{2}V_{1}}{T_{1}V_{2}}$$

T_{1}V_{2} ga bo'lish T_{1}V_{2} ga ko'paytirishni bekor qiladi.

$$P_{2}=\frac{P_{1}T_{2}V_{1}}{T_{1}V_{2}}$$

P_1 uchun yechish

$$\left\{\begin{matrix}P_{1}=\frac{P_{2}T_{1}V_{2}}{T_{2}V_{1}}\text{, }&T_{2}\neq 0\text{ and }V_{1}\neq 0\text{ and }T_{1}\neq 0\\P_{1}\in \mathrm{R}\text{, }&\left(V_{2}=0\text{ or }P_{2}=0\right)\text{ and }V_{1}=0\text{ and }T_{2}\neq 0\text{ and }T_{1}\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini T_{1}T_{2} ga, T_{1},T_{2} ning eng kichik karralisiga ko‘paytiring.

$$T_{2}P_{1}V_{1}=T_{1}P_{2}V_{2}$$

Shartlarni qayta saralash.

$$P_{1}T_{2}V_{1}=P_{2}T_{1}V_{2}$$

Tenglama standart shaklda.

$$T_{2}V_{1}P_{1}=P_{2}T_{1}V_{2}$$

Ikki tarafini T_{2}V_{1} ga bo‘ling.

$$\frac{T_{2}V_{1}P_{1}}{T_{2}V_{1}}=\frac{P_{2}T_{1}V_{2}}{T_{2}V_{1}}$$

T_{2}V_{1} ga bo'lish T_{2}V_{1} ga ko'paytirishni bekor qiladi.

$$P_{1}=\frac{P_{2}T_{1}V_{2}}{T_{2}V_{1}}$$

P_2 uchun yechish

$$\left\{\begin{matrix}P_{2}=\frac{P_{1}T_{2}V_{1}}{T_{1}V_{2}}\text{, }&T_{1}\neq 0\text{ and }V_{2}\neq 0\text{ and }T_{2}\neq 0\\P_{2}\in \mathrm{R}\text{, }&\left(V_{1}=0\text{ or }P_{1}=0\right)\text{ and }V_{2}=0\text{ and }T_{1}\neq 0\text{ and }T_{2}\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini T_{1}T_{2} ga, T_{1},T_{2} ning eng kichik karralisiga ko‘paytiring.

$$T_{2}P_{1}V_{1}=T_{1}P_{2}V_{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$T_{1}P_{2}V_{2}=T_{2}P_{1}V_{1}$$

Tenglama standart shaklda.

$$T_{1}V_{2}P_{2}=P_{1}T_{2}V_{1}$$

Ikki tarafini T_{1}V_{2} ga bo‘ling.

$$\frac{T_{1}V_{2}P_{2}}{T_{1}V_{2}}=\frac{P_{1}T_{2}V_{1}}{T_{1}V_{2}}$$

T_{1}V_{2} ga bo'lish T_{1}V_{2} ga ko'paytirishni bekor qiladi.

$$P_{2}=\frac{P_{1}T_{2}V_{1}}{T_{1}V_{2}}$$