Answer:
C. [tex]2x-4y=0[/tex] and [tex]7x-6y=-24[/tex]
Step-by-step explanation:
We are given the graph of the system of equations given by,
[tex]y=\frac{x}{2}[/tex]
[tex]y=\frac{7x}{6}+4[/tex].
After simplifying the equations, we get,
[tex]y=\frac{x}{2}[/tex] i.e. [tex]2y=x[/tex] i.e. [tex]4y=2x[/tex] i.e. [tex]2x-4y=0[/tex]
And,
[tex]y=\frac{7x}{6}+4[/tex] i.e. [tex]y-\frac{7x}{6}=4[/tex] i.e. [tex]6y-7x=24[/tex] or [tex]7x-6y=-24[/tex]
Hence, we get the system of equations,
[tex]2x-4y=0[/tex] and [tex]7x-6y=-24[/tex]
Now, we will check the point of intersection of the new equations,
Multiplying first equation by 7 and second equation by 2 and then subtracting both equations,
We get,
[tex]14x-28y-14x+12y=48[/tex] gives [tex]-16y=48[/tex] i.e. y = -3
So, 2x-4y=0 gives 2x-4×(-3)=0 i.e. 2x=-12 i.e. x= -6
Thus, the intersection point is (-6,-3).
So, the new system of equation matches the graph.
Hence, option C is correct.
