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Describe the set of points satisfying the inequality 2x+y<=0

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bushin487 | Student | (Level 1) eNoter

Posted April 22, 2012 at 11:06 PM via web

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Describe the set of points satisfying the inequality 2x+y<=0

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Matthew Fonda | eNotes Employee

Posted April 23, 2012 at 1:34 AM (Answer #1)

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To solve this, we'll rewrite the inequality in terms of y, then graph it to visually see the points.

Subtract y from each side:

==> 2x <= -y

Multiply each side by -1. Note that this flips the inequality:

==> -2x >= y

==> y <= -2x

Therefore the set of points that satisfies 2x+y <= 0 is all points on or below the line y = -2x:

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