(k-1)x+(2k+1)y-2-k=0 eching

$$( k - 1 ) x + ( 2 k + 1 ) y - 2 - k = 0$$

k uchun yechish (complex solution)

$$\left\{\begin{matrix}k=-\frac{-x+y-2}{x+2y-1}\text{, }&x\neq 1-2y\\k\in \mathrm{C}\text{, }&x=-1\text{ and }y=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

k-1 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-x+\left(2k+1\right)y-2-k=0$$

2k+1 ga y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-x+2ky+y-2-k=0$$

x ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$kx+2ky+y-2-k=x$$

Ikkala tarafdan y ni ayirish.

$$kx+2ky-2-k=x-y$$

2 ni ikki tarafga qo’shing.

$$kx+2ky-k=x-y+2$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x+2y-1\right)k=x-y+2$$

Ikki tarafini x+2y-1 ga bo‘ling.

$$\frac{\left(x+2y-1\right)k}{x+2y-1}=\frac{x-y+2}{x+2y-1}$$

x+2y-1 ga bo'lish x+2y-1 ga ko'paytirishni bekor qiladi.

$$k=\frac{x-y+2}{x+2y-1}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=-\frac{2ky+y-k-2}{k-1}\text{, }&k\neq 1\\x\in \mathrm{C}\text{, }&y=1\text{ and }k=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

k-1 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-x+\left(2k+1\right)y-2-k=0$$

2k+1 ga y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-x+2ky+y-2-k=0$$

Ikkala tarafdan 2ky ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$kx-x+y-2-k=-2ky$$

Ikkala tarafdan y ni ayirish.

$$kx-x-2-k=-2ky-y$$

2 ni ikki tarafga qo’shing.

$$kx-x-k=-2ky-y+2$$

k ni ikki tarafga qo’shing.

$$kx-x=-2ky-y+2+k$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(k-1\right)x=-2ky-y+2+k$$

Tenglama standart shaklda.

$$\left(k-1\right)x=2+k-y-2ky$$

Ikki tarafini k-1 ga bo‘ling.

$$\frac{\left(k-1\right)x}{k-1}=\frac{2+k-y-2ky}{k-1}$$

k-1 ga bo'lish k-1 ga ko'paytirishni bekor qiladi.

$$x=\frac{2+k-y-2ky}{k-1}$$

k uchun yechish

$$\left\{\begin{matrix}k=-\frac{-x+y-2}{x+2y-1}\text{, }&x\neq 1-2y\\k\in \mathrm{R}\text{, }&x=-1\text{ and }y=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

k-1 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-x+\left(2k+1\right)y-2-k=0$$

2k+1 ga y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-x+2ky+y-2-k=0$$

x ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$kx+2ky+y-2-k=x$$

Ikkala tarafdan y ni ayirish.

$$kx+2ky-2-k=x-y$$

2 ni ikki tarafga qo’shing.

$$kx+2ky-k=x-y+2$$

k'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x+2y-1\right)k=x-y+2$$

Ikki tarafini x+2y-1 ga bo‘ling.

$$\frac{\left(x+2y-1\right)k}{x+2y-1}=\frac{x-y+2}{x+2y-1}$$

x+2y-1 ga bo'lish x+2y-1 ga ko'paytirishni bekor qiladi.

$$k=\frac{x-y+2}{x+2y-1}$$

x uchun yechish

$$\left\{\begin{matrix}x=-\frac{2ky+y-k-2}{k-1}\text{, }&k\neq 1\\x\in \mathrm{R}\text{, }&y=1\text{ and }k=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

k-1 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-x+\left(2k+1\right)y-2-k=0$$

2k+1 ga y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-x+2ky+y-2-k=0$$

Ikkala tarafdan 2ky ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$kx-x+y-2-k=-2ky$$

Ikkala tarafdan y ni ayirish.

$$kx-x-2-k=-2ky-y$$

2 ni ikki tarafga qo’shing.

$$kx-x-k=-2ky-y+2$$

k ni ikki tarafga qo’shing.

$$kx-x=-2ky-y+2+k$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(k-1\right)x=-2ky-y+2+k$$

Tenglama standart shaklda.

$$\left(k-1\right)x=2+k-y-2ky$$

Ikki tarafini k-1 ga bo‘ling.

$$\frac{\left(k-1\right)x}{k-1}=\frac{2+k-y-2ky}{k-1}$$

k-1 ga bo'lish k-1 ga ko'paytirishni bekor qiladi.

$$x=\frac{2+k-y-2ky}{k-1}$$