PLEASE ANSWE

The graph of a system of equations shows the solution to be at (-6, 2). Which two of the following equations could make up this system ? Make sure you choose both equations.

A. 2x - 3y = -6
B. 4x - y = 26
C. 3x + 2y = -14
D. x - y = -2
E. x + y = -4

Step-by-step explanation:

Hi there! First of all I want to say, I do sometimes explain in details and a lot. But if anything I will explain it in the clearest and best way as possible. One more thing is I will have a picture attached! If you can't see it please let me know! So with that in mind, let us begin!

Now, the problem is to figure out which two of these possible system of equations have the coordinate point (-6, 2). A possible way to do this is by replacing "x" and "y" with -6 and 2. How about we do this with each possible equation one at a time.

Choice A:

2x - 3y = -6

2(-6) - 3(2) = -6

-12-6 = -6

-18 = -6

these two are not the same number.

Choice B:

4x - y = 26

4(-6)  - (2) = 26

-24-2= 26

-26= 26

these two are not the same, even though they have the same numbers, the are opposite signs. Positive and Negative numbers are two different things.

Choice C:

3x + 2y = -14

3(-6) + 2(2) = -14

-18 + 4 = -14

-14 = -14

these two equal each other! So choice letter C is one of the equations that has (-6, 2)

Choice D:

x - y = -2

(-6) - (2) = -2

-6-2 = -2

-8 = -2

this equation doesn't not have the same result. So this is a no!

Choice E:

x + y = -4

(-6) + (2) = -4

-6+2= -4

-4= -4

these two are the exact same answers! So choice letter E is the second of the equation that has (-6, 2)!

I hope this answers you question, if not don't hesitate to ask any questions or leave a comment. Again, I have a picture attached with the work!  I hope you have a nice day!

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."