Which quadrant contains no solutions to the system If the system

cherriwood5so3z

cherriwood5so3z

Answered question

2022-06-03

Which quadrant contains no solutions to the system
If the system of inequalities
y 2 x + 1 and y > 0.5 x 1

Answer & Explanation

atoandro8f04v

atoandro8f04v

Beginner2022-06-04Added 7 answers

Every quadrant other than quadrant 4 contains a solution to these. Examples in quadrants 1-3:
Quadrant 1: (1,4)
Quadrant 2: (-2,7)
Quadrant 3: (-3,-1)
The reason why quadrant 4 does not contain any solutions is because y 2 x + 1 has no solutions in the fourth quadrant. We can prove this as follows: Let ( x , y ) be in the fourth quadrant. Thus, x > 0. If ( x , y ) satisfies y 2 x + 1, then y 1. But y 1 does not belong to the fourth quadrant. Hence by contraction, no point in the fourth quadrant satisfies this inequality.

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