GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
x - y = 3 2x = 2y + 6 The system of equations above has how many solu
[#permalink]
03 Mar 2021, 02:30
03 Mar 2021, 02:30
Expert Reply
1
Bookmarks
00:00
Question Stats:
60% (00:24) correct
40% (00:36) wrong based on 15 sessions
Hide Show timer Statistics
x - y = 3
2x = 2y + 6
The system of equations above has how many solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
2x = 2y + 6
The system of equations above has how many solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: x - y = 3 2x = 2y + 6 The system of equations above has how many solu
[#permalink]
03 Mar 2021, 03:34
03 Mar 2021, 03:34
Carcass wrote:
x - y = 3
2x = 2y + 6
The system of equations above has how many solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many
2x = 2y + 6
The system of equations above has how many solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many
For Unique (One solution):
\(\frac{a_1}{a_2} ≠ \frac{b_1}{b_2} ≠ \frac{c_1}{c_2}\)
For No solution (Lines are Parallel):
\(\frac{a_1}{a_2} = \frac{b_1}{b_2} ≠ \frac{c_1}{c_2}\)
For Infinite solutions:
\(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)
Here,
\(\frac{1}{2} = \frac{-1}{-2} = \frac{3}{6}\)
Hence, option E
Re: x - y = 3 2x = 2y + 6 The system of equations above has how many solu
[#permalink]
03 Mar 2021, 06:47
03 Mar 2021, 06:47
Quote:
x - y = 3
2x = 2y + 6
The system of equations above has how many solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many
2x = 2y + 6
The system of equations above has how many solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many
(1) x - y = 3
x = y + 3
2x = 2y + 6
(2) 2x = 2y + 6
So, (1) and 2 are identical.
There are unlimited number of combinations which meet the equation.
For example, x = y + 3
x,y = (0,3), (1,4), (2,5) , (3,6), (4,7)....
Hence the answer is D):
Best,
Gocha
