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(x, y) satisfies |3x - 2y + 4| + |-x + 2y - 2| = 0. What is 2x - y?

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by Max@Math Revolution » Wed May 06, 2020 11:52 pm

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[GMAT math practice question]

(x, y) satisfies |3x - 2y + 4| + |-x + 2y - 2| = 0. What is 2x - y?

A. 1/3
B. -5/2
C. 1
D. -4/3
E. 5/3
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Re: (x, y) satisfies |3x - 2y + 4| + |-x + 2y - 2| = 0. What is 2x - y?

by Max@Math Revolution » Sun May 10, 2020 5:52 pm
=>

Both |3x - 2y + 4| and |-x + 2y - 2| are greater than or equal to 0 and the sum of them is 0, so both of them are 0.
Then we have 3x - 2y + 4 = 0 and -x + 2y - 2 = 0.
Adding the 2 equations together gives us:
3x – 2y + 4 – x + 2y – 2 = 0 + 0
2x + 2 = 0
2x = -2
x = -1
Then 3x – 2y + 4 = 0 becomes:
3(-1) – 2y + 4 = 0
-2y + 1 = 0
-2y = -1
= 1/2
We have x = -1, y = ½.
Thus, we have 2x - y = 2(-1) – ½ = -2 – ½ = -5/2.

Therefore, B is the answer.
Answer: B
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