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

Today we learned how to deal with cases in which neither equation has a variable isolated, such as and .

The two strategies we have so far are:

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

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 or and get an actual number, like .
- 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 .
- 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 .

## 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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