R S Aggarwal and Veena Aggarwal Solutions for Exercise 4: Exercise 3D

For what value of $k$ does the system of equations
$$\begin{gathered} kx + 2y = 5, \\ 3x - 4y = 10 \end{gathered}$$
has no solution?

For what value of $k$ does the system of equations
$$\begin{gathered} x + 2y = 5, \\ 3x + ky + 15 = 0 \end{gathered}$$
has no solution?

For what value of $k$ does the system of equations
$$\begin{gathered} x + 2y = 3, \\ 5x + ky + 7 = 0 \end{gathered}$$
have no solution?
Also, show that there is no value of $k$ for which the given system of equation has infinitely many solutions. 

Find the value of $k$ for which the system of linear equations has an infinite number of solutions:
$\left(k-3\right)x+3y=k$,
$kx+ky=12$.

Find the values of $a$ and $b$ for which the system of linear equations has an infinite number of solutions:
$$\begin{gathered} (a – 1) x + 3y = 2, \\ 6x + (1 – 2b)y = 6 \end{gathered}$$

Find the values of $a$ and $b$ for which the system of linear equations has an infinite number of solutions:
$2x+3y=7$,

$\left(a+b+1\right)x +\left(a+2b+2\right)y=4\left(a+b\right)+1$.

Find the values of $a$ and $b$ for which the system of linear equations has an infinite number of solutions:
$2x + 3y = 7$,
$2ax+\left(a + b\right)y=28$.

Find the value of $k$ for which the system of equations
$5x-3y=0, 2x+ky=0$
has a non zero solution.