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