Linear Equations for Algebra Dummies

Linear equation basics

In case you haven't been paying attention for the past twenty years or so, the U. S. education system is under fire for producing graduates who are too often innumerate¹ and/or scientifically illiterate. Based on some of the freelance rubbish published by their teachers, however, it seems that it isn't the kids' fault. Take a gander, for example, at the dumbassery in "How Are Linear Equations Used In Real Life?" We found it at Sciencing.com, where author Jessica Smith claims to have both an M. Ed. and certification in mathematics. We wonder if her résumé might be a bit inflated...

We wonder because Smith blew it right in the first line of her post:

"Linear equations use one or more variables where one variable is dependent on the other."

Well, Jessica, we hate to burst your bubble, but linear equations have no more than two variables; not to mention that the single-variable form² must also include a constant, e.g., 6x =12. You also didn't bother to mention that you can't have products or powers of variables...

If there are more than two variables, you have a system of linear equations. Solving a system of linear equations is a lot like those puzzles where Mr. Green cannot sit next to Mrs. White and Mr. Plum had the poached salmon. You have to do it in steps and by substitution. Moving right along...
Jessica cribbed a nice example for a linear equation about taxis, which she introduced as,

"...the taxi service charges $9 to pick [you up and] $0.15 per mile for the trip..."

We just included that because Jessica clearly hasn't ridden in a taxi since the '50s! The example she cribbed was $3.00 per pickup and $2.00 per mile, for what it's worth. Smith's example seems contrary to the definition of "real life"...

We'd probably let an ordinary yutz slide on the number of terms in linear equations, but Smith claims to be a teacher. Algebra, unlike "communications," is an exact field; Jessica's sloppy claim of "one or more variables where one variable is dependent on the other"³ is both bad grammar and bad math: hence her award of Dumbass of the Day.

¹ mathematically illiterate
² To be pedantic, all linear equations have two variables: the equation 6x = 12 is in reality 0y = 12 - 6x
³ One variable can't "be dependent on the other" if there's only one variable, right?

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