In the xy plane, does the line with equation y=3x+2 contain the point (r,s)?
1) (3r+2-s)(4r+9-s)=0
2) (4r-6-s)(3r+2-s)=0.
Target question:
Does the line with equation y=3x+2 contain the point (r,s)?
If (r,s) is on the line defined by the equation y=3x+2, then (r,s) must satisfy the equation y=3x+2. In other words, it must be true that s=3r+2
For example: We know that the point (5, 17) is on the line y=3x+2, because when we plug x=5 and y=17 into the equation, we get 17 = 3(5)+2 and the equation holds true.
So, we can reword the target question to be "
Does s = 3r + 2?"
1. (3r+2-s)(4r+9-s) = 0
From this, we know that either (3r+2-s) = 0 or (4r+9-s) = 0
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our new target question is
yes
If (4r+9-s) = 0 then s = 4r+9, in which case the answer to our new target question is
no
Since we get two different answers to the target question, statement 1 is NOT SUFFICIENT
2. (4r-6-s)(3r+2-s) = 0
From this, we know that either (4r-6-s) = 0 or (3r+2-s) = 0
If (4r-6-s)) = 0 then s = 4r-6, in which case the answer to our new target question is
no
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our new target question is
yes
Since we get two different answers to the target question, statement 2 is NOT SUFFICIENT
Statements 1&2 combined: Since (3r+2-s) is the only expression common to both statements, it must be true that 3r+2-s = 0, in which case
s MUST equal 3r+2
As such the answer is
C
Cheers,
Brent
