36/4x-2+8x=12y-3/5 eching

$$\frac { 36 } { 4 x - 2 } + 8 x = \frac { 12 y - 3 } { 5 }$$

y uchun yechish

$$y=-\frac{80x^{2}-34x+87}{12\left(1-2x\right)}$$

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 10\left(2x-1\right) ga, 4x-2,5 ning eng kichik karralisiga ko‘paytiring.

$$5\times 36+8x\times 10\left(2x-1\right)=\left(4x-2\right)\left(12y-3\right)$$

180 hosil qilish uchun 5 va 36 ni ko'paytirish.

$$180+8x\times 10\left(2x-1\right)=\left(4x-2\right)\left(12y-3\right)$$

80 hosil qilish uchun 8 va 10 ni ko'paytirish.

$$180+80x\left(2x-1\right)=\left(4x-2\right)\left(12y-3\right)$$

80x ga 2x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$180+160x^{2}-80x=\left(4x-2\right)\left(12y-3\right)$$

4x-2 ga 12y-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$180+160x^{2}-80x=48xy-12x-24y+6$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$48xy-12x-24y+6=180+160x^{2}-80x$$

12x ni ikki tarafga qo’shing.

$$48xy-24y+6=180+160x^{2}-80x+12x$$

-68x ni olish uchun -80x va 12x ni birlashtirish.

$$48xy-24y+6=180+160x^{2}-68x$$

Ikkala tarafdan 6 ni ayirish.

$$48xy-24y=180+160x^{2}-68x-6$$

174 olish uchun 180 dan 6 ni ayirish.

$$48xy-24y=174+160x^{2}-68x$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(48x-24\right)y=174+160x^{2}-68x$$

Tenglama standart shaklda.

$$\left(48x-24\right)y=160x^{2}-68x+174$$

Ikki tarafini 48x-24 ga bo‘ling.

$$\frac{\left(48x-24\right)y}{48x-24}=\frac{160x^{2}-68x+174}{48x-24}$$

48x-24 ga bo'lish 48x-24 ga ko'paytirishni bekor qiladi.

$$y=\frac{160x^{2}-68x+174}{48x-24}$$

174+160x^{2}-68x ni 48x-24 ga bo'lish.

$$y=\frac{80x^{2}-34x+87}{12\left(2x-1\right)}$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}$$

$$x=-\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}$$

x uchun yechish

$$x=\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}$$

$$x=-\frac{\sqrt{144y^{2}-552y-6671}}{80}+\frac{3y}{20}+\frac{17}{80}\text{, }y\geq 5\sqrt{2}+\frac{23}{12}\text{ or }y\leq \frac{23}{12}-5\sqrt{2}$$