Co- ordinate geomentry----Experts any short cut?

[Chaitanya_1986]

33. In the xy-plane, does the line in question y=3x+2 contain the point (r,s)?
(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0

OA C

[manpsingh87]

33. In the xy-plane, does the line in question y=3x+2 contain the point (r,s)?
(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0

OA C

if the line y=3x+2 contains the point (r,s) than s=3r+2;

1) (3r+2-s)(4r+9-s)=0 ;
now here two cases are possible; case a)3r+2-s=0; 3r+2=s;
case b) 4r+9-s=0; 4r+9=s;
case a) indicates that point (r,s) lies on the line y=3x+2; while case b) doesn't..!!
hence 1 alone is not sufficient to answer the question.

2) (4r-6-s)(3r+2-s)=0 similarly here two cases again are possible;
case a) 4r-6-s=0;
case b) 3r+2-s=0; s=3r+2;

as we can see case b) indicates that point (r,s) lies on the line y=3x+2; while case a) doesn't hence 2 alone is not sufficient to answer the question.

combining 1 and 2) we have common solution 3r+2-s=0 ; s=3r+2; which indicates that point (r,s)lies on the line y=3x+2;
hence C

[HeintzC2]

This is a typical question of 2 equations, 2 unknowns.

We don't need to actually know if (r,s) lies on the line, rather, if can we find out given the information provided. Given that, there's not actually any need to perform any math for this question.

In order to solve simultaneous equations, you must have at least the same number of equations as unknowns, in our case, we have 2 equations with only 2 unknowns per equation. Therefore, yes we can solve this using both equations simultaneously.

The answer is C

33. In the xy-plane, does the line in question y=3x+2 contain the point (r,s)?
(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0

OA C

[spoiler][/spoiler]