Directions: Using the digits 1 to 9 at most one time each, fill in the blanks to create two distinct parallel lines.

__ x + __ y = __

__ x + __ y = __

### Hint

What do the equations of parallel lines have in common?

### Answer

There are many answers but the coefficients of x and y for each line must be multiples of each other. For example, 2x + 3y = 5 and 4x + 6y = 7

Source: Bryan Anderson

There are six blanks but nine numbers. That formulation confuses me a bit.

I see your point, both Robert and I missed that. Clearer wording is needed.

Maybe this would be better.

Directions: Fill in the empty spaces so that you create two distinct parallel lines. You can choose any whole number 1 through 9, but can only use a number once.

Gotcha. Question I don’t know the answer to:

How would the problem and the opportunities to learn be different if 9 changed to 6?

It would cut down on one option set students would have, they would be forced to use 2&4, 3&6- but it would still offer the same learning opportunities.

I wonder if cutting down the options would also lead to less classroom discourse because answers would be too similar.

Good points guys. The directions always seem perfectly clear to me until they don’t. I updated them with this new version.

But parallel lines have the same slope. Why don’t they use this?

Thanks Howard. Hopefully they will have conceptual understanding and approach the problem that way. Unfortunately, many students approach it through brute force.