Solve the following pair of linear equations by the method of elimination: $2x + 5y = 7$ and $4x + 10y = 12$.

Form the pair of linear equations for the following problem,and find their solutions (if they exist) by the elimination method:
$A$ lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ $27$ for a book kept for seven days,while Susy paid ₹ $21$ for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Solve the following pair of linear equations by the method of elimination: $0.3 x + 0.4 y = 1$ and $6 x + 8 y = 20$.

Solve the following pair of equations by the method of elimination:
$11x + 13y = 61$
$13x + 11y = 59$

Use the method of elimination to find the solution of the following pair of linear equations: $5x + 6y = 14$ and $3x - 2y = -14$.

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