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# Paper test question cordinate geometry involving inequality

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Paper test question cordinate geometry involving inequality [#permalink]  10 Sep 2008, 07:55

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Re: Paper test question cordinate geometry involving inequality [#permalink]  10 Sep 2008, 08:09
blover wrote:

2x-3y <= -6
--> y>= 2/3x+6

draw the line y=2/3x+6 on XY plane.
this line cuts throw I,II,III co-ordinatesl.
y>2/3x+6 represents above the line.. which is also not in IV quadrant.

to lie in IV quadrant x should be postive and y shouldbe negative..

when x postive.. y is always +ve.

So Ans IV (E)
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Re: Paper test question cordinate geometry involving inequality [#permalink]  10 Sep 2008, 08:37
x2suresh wrote:
blover wrote:

2x-3y <= -6
--> y>= 2/3x+6

draw the line y=2/3x+6 on XY plane.
this line cuts throw I,II,III co-ordinatesl.
y>2/3x+6 represents above the line.. which is also not in IV quadrant.

to lie in IV quadrant x should be postive and y shouldbe negative..

when x postive.. y is always +ve.

So Ans IV (E)

good one suresh!!!
nice explanation
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Re: Paper test question cordinate geometry involving inequality [#permalink]  10 Sep 2008, 08:45
blover wrote:

alternatively - just plug in:

if you do that, values for (x, y) satisfies for all quadrants but IV.

for ex: if x = 1 and y = -1
2x - 3y = 2+3 = 5 which is greater than -6.

any +ve value for x and -ve value for y donot satisfy the inequality 2x - 3y =< - 6.
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Re: Paper test question cordinate geometry involving inequality [#permalink]  10 Sep 2008, 09:48
LESSON - The General Objective of this lesson is to study linear inequalities.

PERFORMANCE OBJECTIVES - At the end of this lesson the student will be able to graph linear inequalities in two variables.

Linear Inequalities in Two Variables - Linear inequalities can be graphed almost the same way we graph linear equations. Consider the example from the previous section. The graph of the equation

2x - 3y = 6

Every point on the line satisfies the equation

2x - 3y = 6

This means that if you choose any point in the region above or below the line, those points will satisfy one of the following inequalities.

2x - 3y > 6

or

2x - 3y < 6

All you need to do is choose a test point to decide which it is. The test point will usually be (0,0).

Example - Graph the inequality

2x - 3y > 6 .

Step 1 - Solve the related equality for y.

Step 2 - Determine two points by choosing suitable values for x. Let x = 0 and 3. Then y equals -2 and 0 respectively.
Step 3 - Locate these points A(0,-2), B(30) and draw a straight line through them, completely dividing the plane into two regions.
Step 4 - Choose the test point (0,0) and substitute it into the original inequality, to see if it satisfies the inequality.
If it does, the region the test point is in, is the solution.
If it doesn't, the region the test point is not in, is the solution.
2(0) - 3(0) = 0 > 6 No.

Therefore the solution is the region below the line -

2x - 3y = 6.
Re: Paper test question cordinate geometry involving inequality   [#permalink] 10 Sep 2008, 09:48
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