thegmatbeater wrote:In xy plane y=3x+2 contain (r,s)
1) (3r+2-s)(4r+9-s)=0
2) (4r-6-s)(3r+2-s)=0
I think each statement alone is sufficent..But it is wrong!
The point (r,s) is on the line only if s = 3r + 2. If you look at either statement, you have a product of two factors which is equal to zero. That guarantees that
one (not both) of the two factors is equal to zero. So, for example, from 2):
Either 4r-6-s = 0 --> s = 4r - 6
or: 3r+2-s = 0 --> s = 3r + 2
Only in the second case is the point certain to be on the line.
The first statement leads to a similar conclusion. So neither statement is sufficient alone. If you consider the two statements together, the point is either on the line y = 3x +2, or it is simultaneously on the lines y = 4x - 6 and y = 4x +9, which is impossible because these are distinct parallel lines.
