Graph Question

[winnerhere]

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?

[albatross86]

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

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.

[winnerhere]

thanks albatross

thats very clearly put

[sanabk]

Hi Abhay,
Could you please kindly cross check once again if the area is overlapping?


Thanks,
Sana

[albatross86]

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!