given the question: y &#x2212;<!-- − --> 2 &gt; &#x2212;<!-- − --> 3 x

Ryker Stein

Ryker Stein

Answered question

2022-05-20

given the question:
y 2 > 3 x
x 1 y
In the x y plane, if the point with co-ordinates ( 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 ?
1. a < 0
2. b > 0
3. a b > 0
4. a b < 0
5. a > b

Answer & Explanation

Kaylyn Ewing

Kaylyn Ewing

Beginner2022-05-21Added 9 answers

You are given
(1) y 2 > 3 x
(2) x 1 y
Note your second determined inequality of y > x 1 is not correct. It should be y x 1 instead.
Multiplying both sides of (2) by − 3 gives
(3) 3 x 3 + 3 y
Combining with (1) gives
(4) y 2 > 3 + 3 y 2 y < 5 y < 5 2
Moving the values to opposite sides (or multiplying both sides by 1) in (1) gives
(5) 3 x > y + 2
Next, multiplying sides of (4) by 1 gives
(6) y > 5 2
Combining this with (5) gives
(7) 3 x > 5 2 + 2 x > 3 2
Finally, (4) and (7) show, with a = x and b = y, that statements 1, 2 and 3 are never true, but statements 4 and 5 are always true.
Antoine Hill

Antoine Hill

Beginner2022-05-22Added 4 answers

Thanks a lot. Yeah it was a silly mistake from my side. Thanks for pointing it out. It was a basic equation, I was seeing it from the geometry perspective and got confused.

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