Subtraction of two numbers is $5$. If the larger number is $x$,then the smaller number is $y = \ldots \ldots \ldots \ldots$

If the following pair of equations is consistent (unique solution),then find the value of $k$:
$x - ky = 2$
$3x + 2y = -5$

The ages of two friends Ani and Biju differ by $3\, years.$ Ani's father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by $30\, years.$ Find the ages of Ani and Biju.

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

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
The area of a rectangle gets reduced by $9$ square units,if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units,the area increases by $67$ square units. Find the dimensions of the rectangle.

The pair of equations $5x - 15y = 8$ and $3x - 9y = \frac{24}{5}$ has