R. D. Sharma Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 5: EXERCISE 3.5

In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it

$3x-5y=20$

$6x-10y=40$

Find the value of $k$ for which the following system of equations has a unique solution:
$4x+ky+8=0$
$2x+2y+2=0$

Find the value of $k$ for which the following system of equations has a unique solution: $4x-5y=k$; $2x-3y=12$

Find the value of $k$ for which each of the following system of equations have infinitely many solutions :
$2x+3y-5=0$
$6x+ky-15=0$

Find the value of  $k$ for which each of the following system of equations have no solution :
$kx+3y=k-3$
$12x+ky=6 kx+3y=k-3$

Find the values of $a$ and $b$ for which the following system of equations has infinitely many solutions:
$2x+3y=7$
$(a-1)x+(a+2)y=3a$

For which value(s) of $\lambda$, do the pair of linear equations $\lambda x+y={\lambda }^2 \text{and} x+\lambda y=1$ have infinitely many solutions?

For which value(s) of $\lambda$, do the pair of linear equations $\lambda x+y={\lambda }^2 \text{and} x+\lambda y=1$ have a unique solution?