Interesting Rule for Finding X and Y Coordinate intercepts when given a Linear Parameterization In Each Coord Variable

(posted 11/15/2013) - So my new son-in-law was doing some math exercises for class this evening and called to ask why he was not getting an answer that matched his tutoring software. He gave me a problem to work, we did it together and our agreed upon answer didn't match the 'answer-book.'

Well, hubris always brings one low, cause I first tried to do the variable substitution in my head and of course got it wrong (but so did John)! After I actually wrote it down and looked at my algebra I quickly realized I can't subtract and divide very well ... needless to say I did ultimately get the same answer as the tutorial required.

But, to get to the point of this post, I think I discovered a kind of cool alternative to doing parametric substitution to get the desired line and solving for Y with X set to 0; then solving for X with Y set to zero (ie, the intercepts). So, I've included my new approach to finding X, Y intercepts when X and Y are parameterized functions of another variable.

Anyway, here's the solution I worked up -- the only real challenge was verifying the 8-permutations of sign associated with two slope coefficients and the system determinant. The mental exercise was kinda fun, actually...

Writings a bit smallish -- click on the image for full-size viewing.