Option D: [tex](3,14)[/tex] is the point of intersection of the two lines.
Explanation:
The two equations are [tex]y-6 x=-4[/tex] and [tex]y-2 x=8[/tex]
We need to find the point of intersection of the two lines.
Thus, let us solve the equation by substitution method.
From the equation [tex]y-6 x=-4[/tex], we shall determine the value of y, by adding both sides of the equation by 6x.
Hence, we have, [tex]y=6x-4[/tex]
Now, substituting [tex]y=6x-4[/tex] in the equation [tex]y-2 x=8[/tex] , we get,
[tex]6x-4-2 x=8[/tex]
[tex]4x-4=8[/tex]
[tex]4x=12[/tex]
[tex]x=3[/tex]
Substituting [tex]x=3[/tex] in the equation [tex]y-6 x=-4[/tex], we get,
[tex]y-2 (3)=8[/tex]
[tex]y-6=8[/tex]
[tex]y=14[/tex]
Thus, the point of intersection of the two lines is [tex](3,14)[/tex]
Therefore, Option D is the correct answer.
