x(5-x)+2(y-3x)=(x+3)(x-2) eching

$$x ( 5 - x ) + 2 ( y - 3 x ) = ( x + 3 ) ( x - 2 )$$

y uchun yechish

$$y=x^{2}+x-3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x ga 5-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5x-x^{2}+2\left(y-3x\right)=\left(x+3\right)\left(x-2\right)$$

2 ga y-3x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5x-x^{2}+2y-6x=\left(x+3\right)\left(x-2\right)$$

-x ni olish uchun 5x va -6x ni birlashtirish.

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

x+3 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-x-x^{2}+2y=x^{2}+x-6$$

x ni ikki tarafga qo’shing.

$$-x^{2}+2y=x^{2}+x-6+x$$

2x ni olish uchun x va x ni birlashtirish.

$$-x^{2}+2y=x^{2}+2x-6$$

x^{2} ni ikki tarafga qo’shing.

$$2y=x^{2}+2x-6+x^{2}$$

2x^{2} ni olish uchun x^{2} va x^{2} ni birlashtirish.

$$2y=2x^{2}+2x-6$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2y}{2}=\frac{2x^{2}+2x-6}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$y=\frac{2x^{2}+2x-6}{2}$$

2x^{2}+2x-6 ni 2 ga bo'lish.

$$y=x^{2}+x-3$$

x uchun yechish (complex solution)

$$x=\frac{-\sqrt{4y+13}-1}{2}$$

$$x=\frac{\sqrt{4y+13}-1}{2}$$

x uchun yechish

$$x=\frac{-\sqrt{4y+13}-1}{2}$$

$$x=\frac{\sqrt{4y+13}-1}{2}\text{, }y\geq -\frac{13}{4}$$