## Monday, March 12, 2012

### Substitution with Some Flair

Some of my students who prefer not to solve systems by substitution have come up with a new way of substitution that I actually REALLY like. I am going to share it here with you.

Say the problem indicates to solve this following system using substitution (I know, it's totally artificial to prescribe a specific method, but for shared assessment reasons, I want them to still be prepared for questions like this on the semester exam):

2x + 3y = 48
3x - 4y = 4

Basically, some of the kids who dislike substitution have invented a hybrid of the two methods of substitution and elimination. They first scale the equations to get matching terms:

(2x + 3y = 48)*3 becomes 6x + 9y = 144
(3x - 4y = 4)*2 becomes 6x - 8y = 8

If you solve the first equation for 6x, you get 6x = -9y + 144. Then, substitute this into the second equation, you get: (-9y + 144) - 8y = 8. Ingenious! I was impressed that they just invented this hybrid method. It's much easier than getting x = -3y/2 + 24 and plugging that into the second equation to get 3(-3y/2 + 24) - 4y = 4, because the hybrid method they have invented bypasses all of the fractions immediately and still satisfies the problem requirement of applying the concept / skill of substitution. Their method of substitution is so much more elegant than our traditional substitution.

LOVE! Amazing what kids can come up with all by themselves.

I am simply bubbling with excitement to finally start new topics this week! My short attention span really gets the better of me.