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x - y = 3 2x = 2y + 6 The system of equations above has how many solu
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03 Mar 2021, 02:30
03 Mar 2021, 02:30
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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
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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
