Now combing both together we could have either
4r + 9 - s = 0 AND 4r - 6 - s = 0
3r + 2 - s = 0
(reason is obvious, but let me know if it has to be explained)
Please explain this.
Well if the product or 2 numbers is 0 the number1 = 0 OR number2 =0, right ?
Here we have
XY = 0 AND
XZ = 0 if we take Y = 4r + 9 -s and Z = 4r - 6 - s and 3r + 2 - s)
Since X is common in both equations then either X = 0 i.e both expressions become 0 OR X != 0 and Y = 0 as well as Z = 0 for both expressions to be zero. The third case is X, Y, Z are all 0 which is a subset of Y = 0 and Z = 0.