MPM2D Test and some fun questions 2016-09-26

We had our Linear Systems test this morning. In my period 2 class there was quite a bit of extra time for some people (we had a 15 minute presentation in the period 1 class), so I put the following three questions on the board. If you solve them all and email me a solution (answers along with how you got them!) then I’ll have a delicious treat for you in a few days.

  1. How many numbers between 1000 and 9999 have no repeating consecutive digits? (e.g. 7225 is not allowed, but 7252 is)
  2. How many numbers between 1000 and 9999 have no zeros?
  3. How many numbers between 1000 and 9999 have exactly one zero?

These are optional, if that wasn’t already clear :)

MPM2D Solving Problems with Linear Systems 2016-09-21

We had a quiz about solving linear systems. More people were happy with the elimination question than with the substitution question. I’m assuming that’s because we learned elimination more recently. I’ll try to return your quizzes quickly, and I’ll post solutions tomorrow.

We spent the rest of the class looking at some problems that can be solved using linear systems. Here are the problems and some solutions:

solving-some-problems-with-linear-systems-with-solutions

MPM2D Substitution method – special cases – 2016-09-16

We’ve practised finding intersections of lines by substitution when we had a variable isolated already in at least one equation, like y=3x-9 .

Today we learned how to deal with cases in which neither equation has a variable isolated, such as 3x-2y+6=0 and x+4y+1=0 .

The two strategies we have so far are:

  1. Convert one equation into Slope-y-intercept form, then substitute (this is essentially isolating for y
  2. Isolate one equation for x and then substitute (same thing, except it’s for x )

We’ll learn another technique next week.

The Three Possible Outcomes

When you have two linear equations, three things are possible.

  • The two equations represent two lines that are not parallel. When substituting, you’ll be able to solve for x_1 or y_1 and get an actual number, like x_1=\frac{4}{7} .
  • The two equations represent parallel lines that are distinct (they’re not the same line). When substituting you’ll eventually get an equation that cannot be true (such as -6=0 .
  • The two equations represent parallel lines that are identical (they’re the same line). When substituting you’ll eventually get an equation that is always true (such as 5=5 .

The Homework

Complete textbook questions 1 and 2 on Page 26. For both questions please also solve for the intersection points.