F=x+3y+lambda(75-xy) eching

$$F = x + 3 y + \lambda ( 75 - x y )$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=-\frac{3y+75\lambda -F}{1-y\lambda }\text{, }&\lambda =0\text{ or }y\neq \frac{1}{\lambda }\\x\in \mathrm{C}\text{, }&F=75\lambda +\frac{3}{\lambda }\text{ and }y=\frac{1}{\lambda }\text{ and }\lambda \neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\lambda ga 75-xy ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$F=x+3y+75\lambda -\lambda xy$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x+3y+75\lambda -\lambda xy=F$$

Ikkala tarafdan 3y ni ayirish.

$$x+75\lambda -\lambda xy=F-3y$$

Ikkala tarafdan 75\lambda ni ayirish.

$$x-\lambda xy=F-3y-75\lambda$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(1-\lambda y\right)x=F-3y-75\lambda$$

Tenglama standart shaklda.

$$\left(1-y\lambda \right)x=-3y+F-75\lambda$$

Ikki tarafini -y\lambda +1 ga bo‘ling.

$$\frac{\left(1-y\lambda \right)x}{1-y\lambda }=\frac{-3y+F-75\lambda }{1-y\lambda }$$

-y\lambda +1 ga bo'lish -y\lambda +1 ga ko'paytirishni bekor qiladi.

$$x=\frac{-3y+F-75\lambda }{1-y\lambda }$$

x uchun yechish

$$\left\{\begin{matrix}x=-\frac{3y+75\lambda -F}{1-y\lambda }\text{, }&\lambda =0\text{ or }y\neq \frac{1}{\lambda }\\x\in \mathrm{R}\text{, }&F=75\lambda +\frac{3}{\lambda }\text{ and }y=\frac{1}{\lambda }\text{ and }\lambda \neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\lambda ga 75-xy ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$F=x+3y+75\lambda -\lambda xy$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x+3y+75\lambda -\lambda xy=F$$

Ikkala tarafdan 3y ni ayirish.

$$x+75\lambda -\lambda xy=F-3y$$

Ikkala tarafdan 75\lambda ni ayirish.

$$x-\lambda xy=F-3y-75\lambda$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(1-\lambda y\right)x=F-3y-75\lambda$$

Tenglama standart shaklda.

$$\left(1-y\lambda \right)x=-3y+F-75\lambda$$

Ikki tarafini -y\lambda +1 ga bo‘ling.

$$\frac{\left(1-y\lambda \right)x}{1-y\lambda }=\frac{-3y+F-75\lambda }{1-y\lambda }$$

-y\lambda +1 ga bo'lish -y\lambda +1 ga ko'paytirishni bekor qiladi.

$$x=\frac{-3y+F-75\lambda }{1-y\lambda }$$

F uchun yechish

$$F=75\lambda +3y+x-xy\lambda$$