Answer: choice C which is (10,-1)
This means x = 10 and y = -1 pair up together
The graphs cross at this point. See attached graph below.
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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.
