Asap 25 pts + brainliest to right/best answer

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Explanation:

solve for x in the first equation

x+3y = 7

x = -3y+7

Plug this into the second equation

2x - 4y = 24

2(x) - 4y = 24

2(-3y+7) - 4y = 24 ... x replaced with -3y+7

-6y+14 - 4y = 24

-10y+14 = 24

-10y+14-14 = 24-14

-10y = 10

-10y/(-10) = 10/(-10)

y = -1

Use this y value to find x. You can use any equation with x & y in it, but the easiest to use is where we solved for x earlier

x = -3*y + 7

x = -3*(-1) + 7 ... replace y with -1

x = 3 + 7

x = 10

So we have x = 10 and y = -1 pair up together to get the ordered pair (x,y) = (10,-1) as the solution. This is the only solution. The graphs cross at this point. The system is considered to be independent and consistent.

independent because one equation isn't a scalar multiple of the other

consistent because there is at least one solution

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I used the substitution method to get the answer. You can also use elimination to get the answer. Because you have a list of choices, you can guess-and-check choices A through D by plugging in the coordinates. This also helps confirm the answer.

x+3y = 7

10+3(-1) = 7

10-3 = 7

7 = 7 ... works

and

2x-4y = 24

2(10)-4(-1) = 24

20+4 = 24

24 = 24 ... also works

Both equations are true when (x,y) = (10,-1). The solution is confirmed.