Answer: A) no solution
Step-by-step explanation:
The equation of first line = [tex]y=-\dfrac{1}{2}x+4[/tex]
which can be written as : [tex]2y=-x+8[/tex]
[tex]x+2y=8[/tex]
The equation of second line = [tex]y=-\dfrac{1}{2}x-6[/tex]
which can be written as : [tex]x+2y=-12[/tex]
Since , the ratio of the coefficients of x is equal to the ratio of the coefficients of y but not the ratio of the constants .
[tex]\dfrac{1}{1}=\dfrac{2}{2}\neq\dfrac{8}{-12}[/tex]
Therefore , the lines are parallel and do not have any solution.
So , the correct answer is A) no solution.
