Question

Choose the system of equations that matches the following graph:

Answer 1

B but I am not 100% sure

Answer 2

Answer:

C. $2x-4y=0$ and $7x-6y=-24$

Step-by-step explanation:

We are given the graph of the system of equations given by,

$y=\frac{x}{2}$

$y=\frac{7x}{6}+4$.

After simplifying the equations, we get,

$y=\frac{x}{2}$ i.e. $2y=x$ i.e. $4y=2x$ i.e. $2x-4y=0$

And,

$y=\frac{7x}{6}+4$ i.e. $y-\frac{7x}{6}=4$ i.e. $6y-7x=24$ or $7x-6y=-24$

Hence, we get the system of equations,

$2x-4y=0$ and $7x-6y=-24$

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,

$14x-28y-14x+12y=48$ gives $-16y=48$ 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.