(a-1)x+(a+2)y=3a eching

$$( a - 1 ) x + ( a + 2 ) y = 3 a$$

a uchun yechish

$$\left\{\begin{matrix}a=-\frac{2y-x}{x+y-3}\text{, }&x\neq 3-y\\a\in \mathrm{R}\text{, }&x=2\text{ and }y=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$ax-x+\left(a+2\right)y=3a$$

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

$$ax-x+ay+2y=3a$$

Ikkala tarafdan 3a ni ayirish.

$$ax-x+ay+2y-3a=0$$

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

$$ax+ay+2y-3a=x$$

Ikkala tarafdan 2y ni ayirish.

$$ax+ay-3a=x-2y$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x+y-3\right)a=x-2y$$

Ikki tarafini x+y-3 ga bo‘ling.

$$\frac{\left(x+y-3\right)a}{x+y-3}=\frac{x-2y}{x+y-3}$$

x+y-3 ga bo'lish x+y-3 ga ko'paytirishni bekor qiladi.

$$a=\frac{x-2y}{x+y-3}$$

x uchun yechish

$$\left\{\begin{matrix}x=-\frac{ay+2y-3a}{a-1}\text{, }&a\neq 1\\x\in \mathrm{R}\text{, }&y=1\text{ and }a=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$ax-x+\left(a+2\right)y=3a$$

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

$$ax-x+ay+2y=3a$$

Ikkala tarafdan ay ni ayirish.

$$ax-x+2y=3a-ay$$

Ikkala tarafdan 2y ni ayirish.

$$ax-x=3a-ay-2y$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(a-1\right)x=3a-ay-2y$$

Tenglama standart shaklda.

$$\left(a-1\right)x=3a-2y-ay$$

Ikki tarafini a-1 ga bo‘ling.

$$\frac{\left(a-1\right)x}{a-1}=\frac{3a-2y-ay}{a-1}$$

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

$$x=\frac{3a-2y-ay}{a-1}$$