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.

The two-digit number whose digit at the unit's place is $x$ and the digit at the ten's place is $y$ is three times the sum of its digits. This statement is written as $\ldots \ldots \ldots \ldots .$

Comparing the equation $y = -3$ with the standard form $ax + by + c = 0$,we get $a = \dots$

Vijay had some bananas,and he divided them into two lots $A$ and $B$. He sold the first lot at the rate of $Rs. 2$ for $3$ bananas and the second lot at the rate of $Rs. 1$ per banana,and got a total of $Rs. 400$. If he had sold the first lot at the rate of $Rs. 1$ per banana,and the second lot at the rate of $Rs. 4$ for $5$ bananas,his total collection would have been $Rs. 460$. Find the total number of bananas he had.

If $(x, -1)$ is the solution of the linear equation of two variables $3x - y = 7$,then $x = \ldots$

The solution set of $x + 2y - 3 = 0$ and $5x + ky + 7 = 0$ is an empty set. The value of $k$ is .......