r,s

[orel]

in the xy-plane, does the line with the equation y=3x+2 contain the points (r,s)?
(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0

here I thought that the OA should be D. But it is C......

Why?
thanks

[mals24]

Equation of the line: y = 3x + 2
Question asks if (r,s) passes through the line ie if s = 3r + 2 or 3r+2-s = 0?

St 1. (3r+2-s)(4r+9-s)=0

ab = o means either a = or b = 0.
Hence either (3r+2-s)=0 or (4r+9-s)=0...INSUFF

St2. (4r-6-s)(3r+2-s)=0

Same as St 2, either (3r+2-s)=0 or (4r-6-s)=0...INSUFF

Combining 1+2
We know (3r+2-s)=0...SUFF

Answer is C

[orel]

now it makes sense!

thank you!
Feruza

[ooo]

Sorry, I can't follow, how come?

You state that in order that ab = 0 either a = 0 or b = 0

Suppose in statement I (4r+9-s)=0 and in statement II (4r-6-s)=0, would that not leave open the possibility for (3r+2-s) to be UNEQUAL 0 while still satisfying both conditions? Would this not suggest E as an answer?

Thanks for explaining..

[orel]

IN order both statements to be true,

"3r+2-s" must be equal "0".

1. ac=0
2. ad=0

In order both statement to be true "a" must be equal "0"

Hope this helps...

[ooo]

Of course, thank you very much!