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Graph Question

by winnerhere » Sat Jun 26, 2010 11:09 am
Which of the following is true of the areas represented by the inequalities 3x+2y >12 and y+x<3 in the co ordinate plane

a)The are overlapping and finite

b)They are overlapping and infinite

c)They are not overlapping and finite

d)They are not overlapping and infinite

How do you fiind the point of intersection of an inequality?
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by albatross86 » Sat Jun 26, 2010 11:22 am
Plot the lines A: 3x + 2y = 12 and B: x + y = 3 as the border lines for each of these inequality solution sets.

To plot a line on a graph, find out 2 points that satisfy each equation.

Line A: (4,0) and (0,6)
Line B: (3,0) and (0,3)

See attached picture for bad amateurish drawing of these lines :D

Now, you can see clearly that both regions are infinite, they extend indefinitely into the co-ordinate space.

Are they overlapping? Simple test, compare their slopes or try to find a solution for x,y to both those equations.

You'll see that you can actually find a value for x and y that satisfies both equations, or that their slopes are different. This is sufficient to realise that they are overlapping.

Thus the 2 areas are OVERLAPPING AND INFINITE.

Pick B.
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by winnerhere » Sun Jun 27, 2010 1:21 am
thanks albatross :)

thats very clearly put :)
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by sanabk » Wed Aug 18, 2010 1:21 pm
Hi Abhay,
Could you please kindly cross check once again if the area is overlapping?


Thanks,
Sana
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by albatross86 » Wed Aug 18, 2010 7:24 pm
sanabk wrote:Hi Abhay,
Could you please kindly cross check once again if the area is overlapping?


Thanks,
Sana
Sure,

The lines are 3x + 2y = 12 and x + y = 3 solving these two equations gives us x = 6 and y = -3

Thus the point of intersection of the two "border lines" of the inequality is (6,-3) which should be sufficient to see that they are in fact overlapping :)

Hope that helps!
~Abhay

Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide
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