Are the following systems of inequalities the same? Suppose x , y &#x2208;<!-- ∈ --> <mi

Hector Petersen

Hector Petersen

Answered question

2022-06-07

Are the following systems of inequalities the same?
Suppose x , y R, and S 1 is a system of inequalities:
S 1 = { x y 1 x + 2 y 1 3 x 5 y 2 } = { x 1 + y x 2 y 1 x 2 + 5 y 3 }
I eliminate x from S 1 to obtain S 2 :
S 2 = { 1 + y 2 y 1 2 + 5 y 3 2 y 1 } = { 2 y 2 + 5 y 6 y 3 } = { 2 y 5 y }
Therefore, I know that 5 y < . Let S 3 denote the following system of inequalities
S 3 = { x y 1 x + 2 y 1 3 x 5 y 2 5 y < }
My question is, is S 3 = S 1 ?

Answer & Explanation

Donavan Mack

Donavan Mack

Beginner2022-06-08Added 24 answers

Yes, S 3 = S 1 . We need only to show that
5 y <
Therefore, we have,
3 ( x + 2 y ) + 3 x 5 y 3 × 1 + 2
y 5.
But, this notation is problematic.
5 y
The correct one can be written as follows:
5 y <
Or,
y [ 5 , + )

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