Given the linear equation $2x + 3y - 8 = 0$,write another linear equation in two variables such that the geometrical representation of the pair so formed is coincident lines.

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 equations by reducing them to a pair of linear equations:
$\frac{5}{x-1} + \frac{1}{y-2} = 2$
$\frac{6}{x-1} - \frac{3}{y-2} = 1$

Solve the following pair of linear equations by the substitution method:
$\sqrt{2} x + \sqrt{3} y = 0$
$\sqrt{3} x - \sqrt{8} y = 0$

Draw the graphs of the equations $5x - y = 5$ and $3x - y = 3$. Determine the coordinates of the vertices of the triangle formed by these lines and the $y$-axis.

Solve the following pair of linear equations:
$ax + by = c$
$bx + ay = 1 + c$