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.

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