Check whether $(1, 1)$ is a solution of the equation $x - 2y = 4$.

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be Rs. $x$ and that of a pen to be Rs. $y$).

Yamini and Fatima,two students of Class $IX$ of a school,together contributed Rs. $100$ towards the Prime Minister's Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as Rs. $x$ and Rs. $y$.) Draw the graph of the same.

Solve the equation $2x + 1 = x - 3$,and represent the solution$(s)$ on
$(i)$ the number line,
$(ii)$ the Cartesian plane.

Find four different solutions of the equation $x + 2y = 6.$

Find the value of $k$,if $x = 2$,$y = 1$ is a solution of the equation $2x + 3y = k$.