Find the value of $k$ under the given condition for the following pair of linear equations: $2x - 3y = 1$ and $kx + 5y = 7$,such that the system has a unique solution.

Places $A$ and $B$ are $100 \ km$ apart on a highway. One car starts from $A$ and another from $B$ at the same time. If the cars travel in the same direction at different speeds,they meet in $5 \ hours$. If they travel towards each other,they meet in $1 \ hour$. What are the speeds of the two cars?

Solve the following pair of equations by the method of cross-multiplication:
$x + 2y + 1 = 0$
$2x - 3y - 12 = 0$

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
Yash scored $40$ marks in a test,getting $3$ marks for each right answer and losing $1$ mark for each wrong answer. Had $4$ marks been awarded for each correct answer and $2$ marks been deducted for each incorrect answer,then Yash would have scored $50$ marks. How many questions were there in the test?

The value of $c$ for which the pair of equations $cx - y = 2$ and $6x - 2y = 3$ will have infinitely many solutions is

For the linear equation of two variables $ax + by + c = 0$,$\ldots \ldots \ldots \ldots$ is not true.