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28 May 2020, 06:01
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D
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Difficulty:
95%
(hard)
Question Stats:
42% (02:25) correct
58%
(02:10)
wrong
based on 358
sessions
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If x + |y| = 8 and |x| + y = 6, then how many pairs of (x, y) satisfy these two equations?
A. 4
B. 3
C. 2
D. 1
E. 0
Are You Up For the Challenge: 700 Level Questions
A. 4
B. 3
C. 2
D. 1
E. 0
Are You Up For the Challenge: 700 Level Questions
28 May 2020, 06:06
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Bunuel
x + |y| = 8
|x| + y = 6
i.e. x = 7 and y = -1 (I did it with some mental calculation taking all scenarios of x and y being positive and negative)
Answer: Option D
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General Discussion
28 May 2020, 09:05
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Bunuel
Not sure about this one, but here is my approach:
x + |y| = 8 and |x| + y = 6
|y|= 8-x and |x|= 6-y; squaring both equations to remove mod:
\(y^2 = (8-x)^2\) and \(x^2 = (6-x)^2\)
1) \(y^2 = 8^2 -16x + x^2\) and 2) \(x^2 = 6^2 - 12y + y^2\); Substituting value of \(x^2\) from equation 2 in equation 1:
\(y^2 = 8^2 -16\sqrt{(6-y)^2}+6^2 -12y + y^2\)
Solving this we get y= -1 and x= 7; Put in x + |y| = 8 and |x| + y = 6 to check if it satisfies the initial condition.
Condition is satisfied and we got a unique value. So, (7, -1) is a possible value.
There will not be any other value that satisfies x + |y| = 8 and |x| + y = 6 conditions.
Answer: (D) 1
Please can anyone clarify whether my understanding "There will not be any other value that satisfies x + |y| = 8 and |x| + y = 6 conditions." is correct?
