$k$ ની કઈ કિંમત માટે નીચે આપેલ સુરેખ સમીકરણોની જોડને કોઈ ઉકેલ નથી?
$3x + y = 1$
$(2k - 1)x + (k - 1)y = 2k + 1$

Which of the following pairs of linear equations has a unique solution,no solution,or infinitely many solutions? In case there is a unique solution,find it by using the cross-multiplication method.
$3x - 5y = 20$
$6x - 10y = 40$

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 parallel lines.

Solve the following pair of linear equations by the substitution method.
$x+y=14$
$x-y=4$

Form the pair of linear equations for the following problem and find their solution by the substitution method.
$A$ fraction becomes $\frac{9}{11}$ if $2$ is added to both the numerator and the denominator. If $3$ is added to both the numerator and the denominator,it becomes $\frac{5}{6}$. Find the fraction.

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