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Answer: Choice B. (5, 4)</h3>
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Explanation:
Note the matching 4y terms in each equation. The top 4y adds with the -4y down below to get 4y+(-4y) = 0y = 0. This tells us that the y terms go away entirely.
The x terms add to 3x+2x = 5x
The constants on the right hand sides add to 31+(-6) = 25
After adding the equations straight down, we end up with this new equation of 5x = 25
Dividing both sides by 5 leads to x = 5
The answer so far is between B and D.
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Let's use this x value to find y
Plugging x = 5 into the first equation leads to...
3x+4y = 31
3(5) + 4y = 31
15 + 4y = 31
4y = 31-15
4y = 16
y = 16/4
y = 4
Or you could use the second equation
2x - 4y = -6
2(5) - 4y = -6
10 - 4y = -6
-4y = -6-10
-4y = -16
y = -16/(-4)
y = 4
Either way, we get the same y value when x = 5.
So x = 5 and y = 4 pair up together.
Overall, the solution is (x,y) = (5, 4)
