For how many diff erent values of $a$ does the following system have at least two distinct solutions?

$a x+y=0$

$x+(a+10) y=0$

The system of equations $kx + y + z =1$ $x + ky + z = k$ and $x + y + zk = k ^{2}$ has no solution if $k$ is equal to

If the system of equations $x + 2y + 3z = 4 , x + py + 2z = 3 , x + 4y + \mu z = 3$ has an infinite number of solutions , then :

Number of triplets of $a, b \, \& \,c$ for which the system of equations,$ax - by = 2a - b$ and $(c + 1) x + cy = 10 - a + 3 b$ has infinitely many solutions and $x = 1, y = 3$ is one of the solutions, is :

The values of $a$ and $b$, for which the system of equations    $2 x+3 y+6 z=8$   ;  $x+2 y+a z=5$     ;  $3 x+5 y+9 z=b$  has no solution, are:

How many values of $k $ , systeam of linear equations $\left( {k + 1} \right)x + 8y = 4k\;,\;kx + \left( {k + 3} \right)y$$ = 3k - 1$ has no solutions.