Question

Choose the system of equations that matches the following graph:

picture of coordinate plane with line y equals 1 half x and line y equals 7 sixths x plus 4. They intersect at negative 6, negative 3

A. 2x+4y=0 7x-6y= -24
B. 2x-4y=0 7x+6y= -24
C. 2x-4y=0 7x-6y= -24
D.2x+4y=0 7x+6y= -24

Answer 1

b but I am not 100% sure

Answer 2

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

Explanation:

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

`y=(x)/(2)`

`y=(7x)/(6)+4`.

After simplifying the equations, we get,

`y=(x)/(2)` i.e.
`2y=x` i.e.
`4y=2x` i.e.
`2x-4y=0`

And,

`y=(7x)/(6)+4` i.e.
`y-(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.