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20 Systems of Equations
In algebra, you might need to solve two linear equations in two variables and
to solve them simultaneously. Three methods for solving two simultaneous
equations are presented in this chapter. Each has its strong and weak points,
as will be pointed out in the problems.
Solutions to a System of Equations
From Chapter 19, the equation of a linear function has several forms, but
for the purposes of this chapter, the form ax + by = c is preferred. You
know from Chapter 17 that the graph of a linear
equation is a line. When you encounter two such
equations, the basic question you should ask your-
self is, “What are the coordinates of the point of
intersection, if any, of the two lines?”
This question has three possible answers. If
the lines do not intersect, there is no solution. If the two lines intersect,
there is only one solution—an ordered pair (x, y). If the two lines are equal
versions of the same line, then there are infi nitely many solutions—an infi -
nite set of ordered pairs.
Finally, when you are solving two linear equations in two variables, an
example of the standard form of writing them together is
20
3
xy
xy+=y
Remember from Chapter 16 that
the location of a point is an ordered
pair of coordinates such as (x, y).
