y=5x-1/4x+2 eching

$$y= \frac{ 5x-1 }{ 4x+2 }$$

x uchun yechish

$$x=-\frac{2y+1}{4y-5}$$

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -\frac{1}{2} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(2x+1\right) ga ko'paytirish.

$$y\times 2\left(2x+1\right)=5x-1$$

y\times 2 ga 2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4xy+y\times 2=5x-1$$

Ikkala tarafdan 5x ni ayirish.

$$4xy+y\times 2-5x=-1$$

Ikkala tarafdan y\times 2 ni ayirish.

$$4xy-5x=-1-y\times 2$$

-2 hosil qilish uchun -1 va 2 ni ko'paytirish.

$$4xy-5x=-1-2y$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(4y-5\right)x=-1-2y$$

Tenglama standart shaklda.

$$\left(4y-5\right)x=-2y-1$$

Ikki tarafini 4y-5 ga bo‘ling.

$$\frac{\left(4y-5\right)x}{4y-5}=\frac{-2y-1}{4y-5}$$

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

$$x=\frac{-2y-1}{4y-5}$$

-1-2y ni 4y-5 ga bo'lish.

$$x=-\frac{2y+1}{4y-5}$$

x qiymati -\frac{1}{2} teng bo‘lmaydi.

$$x=-\frac{2y+1}{4y-5}\text{, }x\neq -\frac{1}{2}$$

y uchun yechish

$$y=-\frac{1-5x}{2\left(2x+1\right)}$$

$$x\neq -\frac{1}{2}$$