Data Sufficiency

OA: C

Please explain..

Multiplying the three element expressions would give you very nasty unmanageable results, neither of which would be of help in relating the result to our stem. There must be a short cut.

Looking closely at the statement, both of them include the factor (3r+2-s). Since each of these products equals zero, either (3r+2-s) = zero or both of the other expressions equal zero.

Testing the other two first, if they both equal zero they equal each other. Setting them equal we get 15 = 0 - not true so those two do not equal zero.

That means (3r+2-s) = 0 We are asked about the point (r,s) so r must be the x value and s the y value. rewriting (3r+2-s) = 0 we get 3x + 2 - y = 0. Putting that in slope intercept form we get y = 3x+2, which is our original equation so the point (r,s) must satisfy that equation.

thank you Tani for the nice explanation

intercept of the line is ( 0, 2) and ( -2/3 , 0)

we can put this in both the equation and check .
For unique solution we can find a unique set in we club both option 1 and 2