The solution of a pair of equations $y+x=2$ and $y-x=4$ is $(x, y)=\ldots \ldots \ldots . . .$

$A$ person,rowing at the rate of $5 \, km/h$ in still water,takes thrice as much time in going $40 \, km$ upstream as in going $40 \, km$ downstream. Find the speed of the stream in $km/h$.

Obtain the solution of the following pair of equations by the cross-multiplication method: $ax + by = 1$ and $bx + ay = \frac{2ab}{a^2 + b^2}$.

There are some $25$ paise coins and some $50$ paise coins in a bag. The total number of coins is $100$ and the total amount in the bag is Rs. $42.50$. Find the number of coins of each value in the bag.

If $y = \frac{1}{2} x$ and $x + 2y = 8$,then $x = \dots$

Solve the following pairs of equations by the cross-multiplication method:
$x - 3y = -5$
$3x = 7y - 13$