a(q-r)+b(r-p)+d(p-q)=0 eching

$$a ( q - r ) + b ( r - p ) + d ( p - q ) = 0$$

a uchun yechish

$$\left\{\begin{matrix}a=-\frac{dp-bp-dq+br}{q-r}\text{, }&q\neq r\\a\in \mathrm{R}\text{, }&\left(q=p\text{ and }r=p\right)\text{ or }\left(q=r\text{ and }b=d\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

a ga q-r ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$aq-ar+b\left(r-p\right)+d\left(p-q\right)=0$$

b ga r-p ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$aq-ar+br-bp+d\left(p-q\right)=0$$

d ga p-q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$aq-ar+br-bp+dp-dq=0$$

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

$$aq-ar-bp+dp-dq=-br$$

bp ni ikki tarafga qo’shing.

$$aq-ar+dp-dq=-br+bp$$

Ikkala tarafdan dp ni ayirish.

$$aq-ar-dq=-br+bp-dp$$

dq ni ikki tarafga qo’shing.

$$aq-ar=-br+bp-dp+dq$$

Shartlarni qayta saralash.

$$aq-ar=bp-dp+dq-br$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(q-r\right)a=bp-dp+dq-br$$

Ikki tarafini q-r ga bo‘ling.

$$\frac{\left(q-r\right)a}{q-r}=\frac{bp-dp+dq-br}{q-r}$$

q-r ga bo'lish q-r ga ko'paytirishni bekor qiladi.

$$a=\frac{bp-dp+dq-br}{q-r}$$

b uchun yechish

$$\left\{\begin{matrix}b=-\frac{dp+aq-dq-ar}{r-p}\text{, }&r\neq p\\b\in \mathrm{R}\text{, }&\left(a=d\text{ or }q=p\right)\text{ and }r=p\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

a ga q-r ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$aq-ar+b\left(r-p\right)+d\left(p-q\right)=0$$

b ga r-p ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$aq-ar+br-bp+d\left(p-q\right)=0$$

d ga p-q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$aq-ar+br-bp+dp-dq=0$$

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

$$-ar+br-bp+dp-dq=-aq$$

ar ni ikki tarafga qo’shing.

$$br-bp+dp-dq=-aq+ar$$

Ikkala tarafdan dp ni ayirish.

$$br-bp-dq=-aq+ar-dp$$

dq ni ikki tarafga qo’shing.

$$br-bp=-aq+ar-dp+dq$$

Shartlarni qayta saralash.

$$-bp+br=-dp+dq-aq+ar$$

b'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-p+r\right)b=-dp+dq-aq+ar$$

Tenglama standart shaklda.

$$\left(r-p\right)b=ar-aq+dq-dp$$

Ikki tarafini r-p ga bo‘ling.

$$\frac{\left(r-p\right)b}{r-p}=\frac{ar-aq+dq-dp}{r-p}$$

r-p ga bo'lish r-p ga ko'paytirishni bekor qiladi.

$$b=\frac{ar-aq+dq-dp}{r-p}$$