The solution set of $2x + 3y + 5 = 0$ and $4x + 6y + 10 = 0$ is........

Find the value$(s)$ of $p$ for the equations $-3x + 5y = 7$ and $2px - 3y = 1$ if the lines represented by these equations intersect at a unique point.

$x$ years ago,the sum of the ages of a mother,father,and two children was $y$ years. What will be the sum of their ages after $z$ years?

Solve the following pair of equations by the cross-multiplication method:
$\frac{x}{a} - \frac{y}{b} = 0$
$ax + by = a^2 + b^2$

There are some students in the two examination halls $A$ and $B$. To make the number of students equal in each hall,$10$ students are sent from $A$ to $B$. But if $20$ students are sent from $B$ to $A$,the number of students in $A$ becomes double the number of students in $B$. Find the number of students in the two halls.

Prashant purchases $2$ mobiles and $3$ memory cards for Rs. $6500$. The cost of one mobile and one memory card is Rs. $2950$. Represent this as a pair of linear equations in two variables.