Question

P(m,n) (m,n are natural no.) is any point in the interior of the two lines 2x+y-2=0 and 4x+5y-20=0, then find the possible no. of positions of P.

Answer 1

What does it mean by interior?

Answer 2

internal region containing x-axis.

Answer 3

i have found the ans. by plotting graph.
Is there any other method?

Answer 4

I'm sorry, I'm just confused possibly. The two equations are both lines, and they intersect at a single point, (-5/3, 16/3). It wasn't clear what sort of point P(m,n) would be. Even knowing the graph, I guess I just don't understand what the interior region containin the x-axis means in this case.

Answer 5

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyLTJ4IiwiY29sb3IiOiIjMDAwMDAwIn0seyJ0eXBlIjowLCJlcSI6IigyMC00eCkvNSIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi04LjQ5MjgxMDk1Nzk2NzMyOSIsIjcuNzU3MTg5MDQyMDMyNjA0IiwiLTQuOTEyMjIwMDI3MDIzMzM4IiwiNS4wODc3Nzk5NzI5NzY2MjEiXSwiZ3JpZCI6WyIxIiwiMSJdLCJzaXplIjpbNzUwLDUwMF0sImF4ZXNjb2xvciI6IiMyNDFGMUYiLCJsYWJlbHNjb2xvciI6IiMxMzM4RjAifV0-

Answer 6

points in 1st quadrant between the given lines.

Answer 7

maybe it's any point in the region between the two lines and the x-axis and y-axis... yes, just like you said just now...

Answer 8

since they are natural numbers, I would assume it is those points with integer coordinates that are fully in that region. Not sure about points on the borders, like (5,0) and (1,0)...

But I don't see any method other than graphing that you could solve this.

Answer 9

I didn't know about FooPlot... will have to remember that site :)