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y 2 > 3x x < 1 y In the xy plane, if the point with co-ordinate
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04 Sep 2023, 01:24
04 Sep 2023, 01:24
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50% (02:13) correct
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y – 2 > – 3x
x < –1 – y
In the xy plane, if the point with coordinates (a, b) lies in the solution set of the system of inequalities above, which of the following relationships between a and b must be true?
Indicate all that apply
A. a < 0
B. b > 0
C. ab > 0
D. ab < 0
E. a > b
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
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x < –1 – y
In the xy plane, if the point with coordinates (a, b) lies in the solution set of the system of inequalities above, which of the following relationships between a and b must be true?
Indicate all that apply
A. a < 0
B. b > 0
C. ab > 0
D. ab < 0
E. a > b
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
\(\Longrightarrow\) ALL the GRE Quant and Verbal Practice Directories in ONE place (2023)
\(\Longrightarrow\) Best GRE Test Books of 2023
Re: y 2 > 3x x < 1 y In the xy plane, if the point with co-ordinate
[#permalink]
05 Sep 2023, 09:58
05 Sep 2023, 09:58
1
Put a and b in the equations, therefore equation would be
b-2 > -3a => 3a+b > 2
a<-1-b => a+b<-1 can also be written as -a-b>1
add 1 and 2
2a>3 => a > 3/2
Now substitute value of a in eq 1
b> 2-3a
Since a is always positive and 3a > 2, therefore b would always be negative
Hence d and e are the answers
b-2 > -3a => 3a+b > 2
a<-1-b => a+b<-1 can also be written as -a-b>1
add 1 and 2
2a>3 => a > 3/2
Now substitute value of a in eq 1
b> 2-3a
Since a is always positive and 3a > 2, therefore b would always be negative
Hence d and e are the answers
Re: y 2 > 3x x < 1 y In the xy plane, if the point with co-ordinate
[#permalink]
05 Oct 2023, 08:49
05 Oct 2023, 08:49
Carcass wrote:
y – 2 > – 3x
x < –1 – y
In the xy plane, if the point with coordinates (a, b) lies in the solution set of the system of inequalities above, which of the following relationships between a and b must be true?
Indicate all that apply
A. a < 0
B. b > 0
C. ab > 0
D. ab < 0
E. a > b
x < –1 – y
In the xy plane, if the point with coordinates (a, b) lies in the solution set of the system of inequalities above, which of the following relationships between a and b must be true?
Indicate all that apply
A. a < 0
B. b > 0
C. ab > 0
D. ab < 0
E. a > b
Another way to solve this is use simultaneous equations and find the point of intersection for the two lines and then see which options apply to this point. Only options D and E apply.
