m+5n=m-n/12m eching

$$m + 5 n = \frac { m - n } { 12 m }$$

n uchun yechish

$$n=-\frac{m\left(12m-1\right)}{60m+1}$$

$$m\neq -\frac{1}{60}\text{ and }m\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 12m ga ko'paytirish.

$$12mm+5n\times 12m=m-n$$

m^{2} hosil qilish uchun m va m ni ko'paytirish.

$$12m^{2}+5n\times 12m=m-n$$

60 hosil qilish uchun 5 va 12 ni ko'paytirish.

$$12m^{2}+60nm=m-n$$

n ni ikki tarafga qo’shing.

$$12m^{2}+60nm+n=m$$

Ikkala tarafdan 12m^{2} ni ayirish.

$$60nm+n=m-12m^{2}$$

n'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(60m+1\right)n=m-12m^{2}$$

Ikki tarafini 60m+1 ga bo‘ling.

$$\frac{\left(60m+1\right)n}{60m+1}=\frac{m\left(1-12m\right)}{60m+1}$$

60m+1 ga bo'lish 60m+1 ga ko'paytirishni bekor qiladi.

$$n=\frac{m\left(1-12m\right)}{60m+1}$$

m uchun yechish (complex solution)

$$\left\{\begin{matrix}\\m=\frac{\sqrt{3600n^{2}-168n+1}}{24}-\frac{5n}{2}+\frac{1}{24}\text{, }&\text{unconditionally}\\m=-\frac{\sqrt{3600n^{2}-168n+1}}{24}-\frac{5n}{2}+\frac{1}{24}\text{, }&n\neq 0\end{matrix}\right,$$

m uchun yechish

$$\left\{\begin{matrix}m=-\frac{\sqrt{3600n^{2}-168n+1}}{24}-\frac{5n}{2}+\frac{1}{24}\text{, }&n\geq \frac{\sqrt{6}}{150}+\frac{7}{300}\text{ or }\left(n\neq 0\text{ and }n\leq -\frac{\sqrt{6}}{150}+\frac{7}{300}\right)\\m=\frac{\sqrt{3600n^{2}-168n+1}}{24}-\frac{5n}{2}+\frac{1}{24}\text{, }&n\geq \frac{\sqrt{6}}{150}+\frac{7}{300}\text{ or }n\leq -\frac{\sqrt{6}}{150}+\frac{7}{300}\end{matrix}\right,$$