x^2+4xy=5y eching

$$x ^ { 2 } + 4 x y = 5 y$$

y uchun yechish

$$y=-\frac{x^{2}}{4x-5}$$

$$x\neq \frac{5}{4}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 5y ni ayirish.

$$x^{2}+4xy-5y=0$$

Ikkala tarafdan x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$4xy-5y=-x^{2}$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(4x-5\right)y=-x^{2}$$

Ikki tarafini 4x-5 ga bo‘ling.

$$\frac{\left(4x-5\right)y}{4x-5}=-\frac{x^{2}}{4x-5}$$

4x-5 ga bo'lish 4x-5 ga ko'paytirishni bekor qiladi.

$$y=-\frac{x^{2}}{4x-5}$$

x uchun yechish (complex solution)

$$x=\sqrt{y\left(4y+5\right)}-2y$$

$$x=-\sqrt{y\left(4y+5\right)}-2y$$

x uchun yechish

$$x=\sqrt{y\left(4y+5\right)}-2y$$

$$x=-\sqrt{y\left(4y+5\right)}-2y\text{, }y\leq -\frac{5}{4}\text{ or }y\geq 0$$