Use the method of elimination to find the solution of the following pair of linear equations: $2x + y = 4$ and $x + 3y = 7$.

The solution of the pair of equations $x + 2y = 5$ and $3x + 5y = 13$ is ...........

Form the pair of linear equations for the following problem,and find their solutions (if they exist) by the elimination method:
If we add $1$ to the numerator and subtract $1$ from the denominator,a fraction reduces to $1$. It becomes $\frac{1}{2}$ if we only add $1$ to the denominator. What is the fraction?

Solve the following pairs of equations:
$4x + \frac{6}{y} = 15$
$6x - \frac{8}{y} = 14, y \neq 0$

If the sum of two numbers is $20$ and their difference is $8,$ then the larger number is ...........

Solve the following pairs of equations by the method of elimination:
$\frac{x}{2} + \frac{3y}{5} + 1 = 0$
$\frac{x}{2} + \frac{y}{3} - \frac{1}{3} = 0$