By the method of substitution,solve the following pair of linear equations: $3x - 7y = 18, 6x - 14y = 12$.

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

Solve the following pairs of equations by the method of elimination:
$5x - 3y = 1$
$2x + 5y = 19$

The cost of $2\,kg$ of apples and $1\,kg$ of grapes on a day was found to be Rs. $160$. After a month,the cost of $4\,kg$ of apples and $2\,kg$ of grapes is Rs. $300$. Represent this situation as a pair of linear equations in two variables.

Solve the following pair of linear equations: $2(3u - v) = 5uv$ and $2(u + 3v) = 5uv$.

The solution set of a pair of equations $5x - 5y = -5$ and $\frac{3x}{2} - \frac{3y}{2} + \frac{3}{2} = 0$ is.........