In the xy - plane, does the line with equation y = 3x + 2 contain the point (r,s)?

Question

1) (3r + 2 -s)(4r + 9 -s) = 0
2) (4r - 6 - s)(3r + 2 -s) = 0

Choice A: Statement 1 is sufficient by itself
Choice B: Statement 2 is sufficient by itself
Choise C: Need both statements together to find the answer
Choice D: Either statement is sufficient by itself
Choice E: Neither statement.

Please select the best choice for this question and explain why you picked it.

Answer 1

If Statement 1 is true, then either
(1.1) 3r + 2 - s = 0, or
(1.2) 4r + 9 - s = 0.
If (1.1) is true, then s=3r+2 which means (r,s) are on the line y=3x+1.
If (1.2) is true, then s=4r + 9 which is not the desired line.
Therefore, Statement 1 by itself is not enough.

You can show the same way that Statement 2 by itself isn't enough.
Statement 2 <---> (2.1) or (2.2) where
(2.1) s=4r-6
(2.2) s=3r+2

But if both statements are true, then:
[(1.1) or (1.2)] AND [(2.1) or (2.2)] is true
[(1.1) or (1.2)] AND [(2.1) or (1.1)] is true because (2.2) is the same as (1.1)
(1.1) or [(1.2)] AND (2.1)] is true
(1.2) s = 4r + 9 and (2.1) s=4r-6 cannot both be true, therefore
(1.1) or (false) is true
(1.1) is true.

So if both statements are true, s=3r+2. Answer:C.

Answer 2

(r, s) belongs to y = 3x + 2:
s = 3r+2

1)
(3r + 2 -s)(4r + 9 -s) = 0
(s -s)(4r + 9 -3r -2) = 0
0(r + 7) = 0

Right

2)
(4r - 6 - s)(3r + 2 -s) = 0
(4r - 6 -3r-2)(s -s) = 0
(r - 8)0 = 0

Right

Answer: Choice D: Either statement is sufficient by itself.

₢

Answer 3

On what basis you got the expressions [4r+9-s] and [4r-6-s]. If r,s has to be a point on line given then it has to satisfy the equation. We at least need two equations to solve for r and s. Then we substitute r,s in the equation. Only then we can confirm if r,s lies on the line.

Answer 4

Maybe I could be wrong , but I say D.
Because assuming (r,s) is in y=3x+2, then s=3r+2.
So, (3r+2-s), which is in both 1 and 2, gives you (3r+2-3r-2) = 0.
So, it seems either statement is sufficient by itself.

Answer 5

choice C

simultaneous equations to solve for 2 variables

Answer 6

Choice C.

To find the value of two variables you will need two equations with those variables in them. The same goes for n variables, you will need n equations to solve for all of them.

Answer 7

B.... Because I always select B and it always works.