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Sagot :
Given:
The system of equations is
[tex]3y=\dfrac{3}{2}x+6[/tex]
[tex]\dfrac{1}{2}y-\dfrac{1}{4}x=3[/tex]
To find:
The solution of the given system of equations.
Solution:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
We have,
[tex]3y=\dfrac{3}{2}x+6[/tex] ...(i)
[tex]\dfrac{1}{2}y-\dfrac{1}{4}x=3[/tex] ...(ii)
Rewritten the given equation in slope intercept forms.
In equation (i), divide both sides by 3.
[tex]y=\dfrac{1}{2}x+2[/tex]
Slope of this line is [tex]\dfrac{1}{2}[/tex] and y-intercept is 2.
In equation (ii), multiply both sides by 2 and isolate y variable.
[tex]y-\dfrac{1}{2}x=6[/tex]
[tex]y=\dfrac{1}{2}x+6[/tex]
Slope of this line is [tex]\dfrac{1}{2}[/tex] 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.
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