Draf

{\color{Blue} \begin{matrix} (a)\; 3x-2y = 4 \\ \, \, \, \, \, \, \, \, \, 6x -4y = 9 \end{matrix} }
{\color{Blue} \begin{matrix} 3x-2y = 4 \\ 6x -4y = 9 \end{matrix} }

Consider the linear system

Suppose there exists (x, y) solution of the system above. Then we have that 3x – 2y = 4 and 6x-4y = 9 which gives us 2.(3x – 2y) – (6x – 4y) =2.4 – 9. Since 2(3x – 2y) – (6x – 4y) = 6x – 4y – 6x + 4y = 0 and 2.4 – 9 = 8 – 9 =-1 we have that 0 =  -1 which is a contradiction. Hence the system has no solution and therefore the lines whose equation are 3x – 2y = 4 and 6x – 4y = 9 have no intersection. Here is sketch of the lines 3x – 2y = 4 and 6x – 4y = 9.

{\color{Blue} \begin{matrix} (b)\; 2x-4y = 1 \\ \, \, \, \, \, \, \, \, \, 4x -8y = 2 \end{matrix} }
{\color{Blue} \begin{matrix} (c)\; x-2y = 0 \\ \, \, \, \, \, \, \, \, \, x -4y = 8 \end{matrix} }