Given:
The system of equations is
![3y=\dfrac{3}{2}x+6](https://tex.z-dn.net/?f=3y%3D%5Cdfrac%7B3%7D%7B2%7Dx%2B6)
![\dfrac{1}{2}y-\dfrac{1}{4}x=3](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7Dy-%5Cdfrac%7B1%7D%7B4%7Dx%3D3)
To find:
The solution of the given system of equations.
Solution:
The slope intercept form of a line is
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where, m is slope and b is y-intercept.
We have,
...(i)
...(ii)
Rewritten the given equation in slope intercept forms.
In equation (i), divide both sides by 3.
![y=\dfrac{1}{2}x+2](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B2%7Dx%2B2)
Slope of this line is
and y-intercept is 2.
In equation (ii), multiply both sides by 2 and isolate y variable.
![y-\dfrac{1}{2}x=6](https://tex.z-dn.net/?f=y-%5Cdfrac%7B1%7D%7B2%7Dx%3D6)
![y=\dfrac{1}{2}x+6](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B2%7Dx%2B6)
Slope of this line is
and y-intercept is 6.
Since slopes of both lines are same but the y-intercepts are different, therefore, the lines are parallel and the system of equations have no solution.
Therefore, the correct option is c.