In Prime Minister's cabinet, a total of$56$Ministers include Cabinet Rank Ministers and Ministers of State. Number of Ministers of State is $5$ more than twice the Cabinet Rank Ministers. Represent this situation algebraically and graphically.

In the given pair of linear equations, identify whether the solution is a unique solution, no solution, or infinitely many solutions.

$2x+5y=17$

$5x+3y=14$

In the given pair of linear equations, identify whether the solution is a unique solution, no solution, or infinitely many solutions.

 $3x-5y=7$

$6x-10y=3$

In the given pair of linear equations, identify whether the solution has: Unique Solution / No Solution / Infinite Solutions.

$4x+6y=7$

$12x+18y=21$

Find the value of '$k$' for which the following system of linear equations has no solution:

$kx + 2y = 5$

$3x - 4y =10$

Find the value of $k$ for which the following system of linear equations has no solution:

$3x+2y=1$

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

Find the value of '$k$' (Positive values only) for which the following system of linear equations has no solution :

$kx+3y=k-3$

$12x+ky=k$

Find the value of $k$ for which the following system of linear equations has an infinite number of solutions.

$2x+3y=7$

$\left(k-1\right)x+\left(k+2\right)y=3k$

Find the value of $k$ for which the following systems of linear equations have an infinite number of solutions.

$2x+ky=3$

$\left(k+5\right)x+25y=2k+5$