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18 Oct 2018, 02:02
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
70% (01:05) correct
30%
(01:13)
wrong
based on 349
sessions
History
Date
Time
Result
Not Attempted Yet
The system of equations has how many solutions?
3x - 6y = 9
2y - x - 3 = 0
A. None
B. Exactly 1
C. Exactly 2
D. Exactly 3
E. Infinitely many
3x - 6y = 9
2y - x - 3 = 0
A. None
B. Exactly 1
C. Exactly 2
D. Exactly 3
E. Infinitely many
18 Oct 2018, 02:28
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Bunuel
By rearranging and deducing two equations, we get
=>3x-6y=9
=>x-2y=3 ---- Equation 1
=>2y-x-3=0
=>x-2y+3=0
=>x-2y=-3 -------Equation 2
Now please note the following rules:
if two equation are given as :
ax+by=c
dx+ey=f
then if
a/d=b/e=c/f, then equations have infinite no. of solutions,
a/d not equal to b/e, then equations have a unique solution and
a/d=b/e not equal to c/f, then equations have no solution
Now applying above rules to equation 1 & 2, mentioned above
we get, 1/1=-2/-2 not equal to 3/-3
Hence, these equation have no solution. So, option A should be the correct option.
Updated on: 22 Mar 2025, 08:18
Originally posted by BrentGMATPrepNow on 05 Aug 2020, 10:09.
Last edited by Krunaal on 22 Mar 2025, 08:18, edited 2 times in total.
Last edited by Krunaal on 22 Mar 2025, 08:18, edited 2 times in total.
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Bunuel
Given:
3x - 6y = 9
2y - x - 3 = 0
Rewrite the bottom equation as follows:
3x - 6y = 9
-x + 2y = 3
Multiply both sides of the the bottom equation by -3 to get:
3x - 6y = 9
3x - 6y = -9
Subtract the bottom equation from the top equation to get: 0x + 0y = 18
NOTE: I know this is an odd way to express the left side of the equation, but it's the easiest way to see why there are zero solutions.
Answer: A
Cheers,
Brent
