M L Aggarwal Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: Exercise 3.1

Find the value(s) of $k$ for which the following pairs of linear equations have infinite solutions:

$kx+4y=k-4$

$16x+ky=k$

Find the value(s) of $k$ for which the following pairs of linear equations have infinite solutions:

$2x+3y=7$

$(k+1)x+(2k-1)y=4k+1$

Find the value(s) of $k$ for which the following pairs of linear equations have infinite solutions:

$2x+3y-7=0$

$(k-1)x+(k+1)y=3k-1$

For what value of $k$, the following pair of linear equations has a unique solution:
$2x+ky=1, 3x-5y=7$

Find the value(s) of $p$ for which the lines represented by the following pair of linear equations intersect at a unique point:
$-3x+5y=7$ and $2px-3y=1$.

For what value(s) of $k$, the following pair of linear equations has no solution:
$kx+3y=k-3, 12x+ky=k$

For what value(s) of $k$, the following pair of linear equations has infinitely many solutions:
$kx+3y=k-3, 12x+ky=k$

For what value(s) of $k$, the following pair of linear equations has unique solution:

$kx+3y=k-3, 12x+ky=k$