Solve the following pair of linear equations:
$21x + 47y = 110$
$47x + 21y = 162$

Obtain a pair of linear equations in two variables from the following information: Three years ago,the age of Abhishek was four times the age of Sweta. After five years,the age of Abhishek will be two times the age of Sweta.

If $4x - 12y = 20$,then $5x - 15y = \ldots$

$A$ railway half ticket costs half the full fare,but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from station $A$ to $B$ costs $Rs. 2530$. Also,one reserved first class ticket and one reserved first class half ticket from $A$ to $B$ costs $Rs. 3810$. Find the full first class fare from station $A$ to $B$,and also the reservation charges for a ticket (in $Rs.$).

$A$ line $x-2y=2$ intersects the $Y$-axis at..........

Determine,algebraically,the vertices of the triangle formed by the lines $5x - y = 5$,$x + 2y = 1$,and $6x + y = 17$.