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# In a rectangular coordinate system, which quadrant, if any

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Intern
Joined: 16 Aug 2003
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In a rectangular coordinate system, which quadrant, if any [#permalink]  21 Oct 2003, 16:56
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In a rectangular coordinate system, which quadrant, if any contains no point (x,y) that satisfies the inequality 2x - 3y <= -6? (Ans. III Quadrant)

What is the most elegant way to solve this inequality?

My solution was to plot the line that satisfies this equation. I am sure there is a better way to solve this inequality. Help ?
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Joined: 11 Mar 2003
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Manager
Joined: 27 Jul 2003
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simplify the equation
2x-3y <= -6
-3y <= -(6+2x)
multiply by -1 and flip the sign
3y >= 6+2x
y >= 2/3x + 2

Plot a T Chart for x and y values
for x = -6, y= -2
x=-3 , y = 0
x= 0 , y=2
x= 3 , y=4
x=6, y=6

If you plot a graph with these values . No points are lying the IV quadrant

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