Post 13: Elimination as a Solving Strategy

(by Mark O. with help from Sage the intrepid student dog)

A gap in the path stretches too wide to cross. The only way over are two creatures standing at its edge. Each are built out of a stack of mismatched blocks. One is short and squat, the other tall and thin. Neither can lie down flat across the gap alone without leaving a dangerous, uneven step in the middle. The only way to make a solid bridge is to get the two creatures to exactly the same size first.

Problem: Scaling before you subtract

Sometimes the matching term in two equations doesn't line up right away. Before you can cancel it out, you may need to multiply one whole equation by a number first, every term, not just one.

Which number should you multiply the first equation by, so the x terms match and can be cancelled?

x + 2y = 8

3x + y = 9

A) 2 B) 3

(It's B.)

Let's take a look at why:

Sage is working on the problem below.

Practice it yourself:

(Hold control and press enter when the cursor is on a line to add more math lines)

The bridge holds steady as the kids cross one by one, patting the creature's side on the way past. Sage scaled the smaller creature up, block by block, until it matched the other exactly, and their mismatched parts settled into one calm, sturdy shape the moment they lined up. Off to the side, the shadowy figure had quietly resized the second creature too, calming the pair faster than Sage expected. Sage looks back once, sure something helped this time, but the figure has already slipped back into the rubble.

Catch your algebra mistakes before they cost you

The scratchpad in this guide runs on moment.of.math — a free Chrome extension that checks your algebra line by line, on any problem. It can generate new variations problems, so you can get as much practice as you need. On many homework sites, it automatically detects the math on the page, so you don't have to copy anything over. Try it on tonight's homework.

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