(Quick response needed) The graph shows the system of equations below. 2 x minus 3 y = negative 6. y = negative one-third x minus 4

Which statement is supported by the graph?

A. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).

B. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is ( –2, –6).

C. The red line represents the equation 2x-3y=6, and the solution to the system of equations is (2, –4).

D. The red line represents the equation 2x-3y=6, and the solution to the system of equations is (–4, 2).

A. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).

Step-by-step explanation:

Here we have the system:

2x - 3y = -6

y = -(1/3)*x - 4

First, remember that if the slope is negative, then the equation is decreasing.

So, for the second equation, as x increases, y decreases, then the line of the second equation is the red one (because the red one decreases).

So the blue one represents the equation 2x - 3y = -6

Also remember that the solution of a system of equations is the point where the graphs of the equations intersect, here we can see that the intersection happens at the point (-6, - 2)

This means that the solution of the system is  (-6, - 2)

From this, we can see that the correct option is:

A. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.