From a bus stand in Bangalore,if we buy $2$ tickets to Malleswaram and $3$ tickets to Yeshwanthpur,the total cost is ₹ $46$; but if we buy $3$ tickets to Malleswaram and $5$ tickets to Yeshwanthpur,the total cost is ₹ $74$. Find the fares from the bus stand to Malleswaram and to Yeshwanthpur.

(N/A) Let ₹ $x$ be the fare from the bus stand in Bangalore to Malleswaram,and ₹ $y$ be the fare to Yeshwanthpur. From the given information,we have:
$2x + 3y = 46$,i.e.,$2x + 3y - 46 = 0$ $...(1)$
$3x + 5y = 74$,i.e.,$3x + 5y - 74 = 0$ $...(2)$
To solve the equations by the cross-multiplication method,we use the coefficients as follows:
$\frac{x}{(3)(-74) - (5)(-46)} = \frac{y}{(-46)(3) - (-74)(2)} = \frac{1}{(2)(5) - (3)(3)}$
i.e.,$\frac{x}{-222 + 230} = \frac{y}{-138 + 148} = \frac{1}{10 - 9}$
i.e.,$\frac{x}{8} = \frac{y}{10} = \frac{1}{1}$
Thus,$\frac{x}{8} = 1$ and $\frac{y}{10} = 1$,which gives $x = 8$ and $y = 10$.
Hence,the fare from the bus stand in Bangalore to Malleswaram is ₹ $8$ and the fare to Yeshwanthpur is ₹ $10$.