Answer: The correct option is (C) No solution.
Step-by-step explanation: We are given to find the solution of the following system of equations :
[tex]3y=\dfrac{3}{2}x+6~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\\dfrac{1}{2}y-\dfrac{1}{4}x=3~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Dividing equation (i) by 3 on both sides, we get
[tex]\dfrac{3y}{3}=\dfrac{3}{3\times2}x+\dfrac{6}{3}\\\\\\\Rightarrow y=\dfrac{1}{2}x+2~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of y from equation (iii) in equation (ii),we get
[tex]\dfrac{1}{2}y-\dfrac{1}{4}x=3\\\\\\\Rightarrow \dfrac{1}{2}\left(\dfrac{1}{2}x+2\right)-\dfrac{1}{4}x=3\\\\\\\Rightarrow \dfrac{1}{4}x+1-\dfrac{1}{4}x=3\\\\\Rightarrow 1=3,[/tex]
which CANNOT be true.
So, the given system of equations will have no solution.
Option (C) is CORRECT.
