Solve the following pair of linear equations using the cross-multiplication method:
$5x + 2y = 10$
$4x + 3y - 1 = 0$

In a two-digit number, the digit at the unit's place is $(2x - 1)$ and the digit at the ten's place is $(2x + 1)$. Then, that number is:

$A$ pair of linear equations which has a unique solution $x=2, y=-3$ is

$x$ is larger in two numbers $x$ and $y$. Two times the larger number is $4$ more than five times the smaller number. The equation form of this data is $\ldots \ldots \ldots \ldots$

$A$ 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 $Rs.$).

Is it true to say that the pair of equations $-x + 2y + 2 = 0$ and $\frac{1}{2}x - \frac{1}{4}y - 1 = 0$ has a unique solution? Justify your answer.