Algebra Know-It-ALL

In this chapter, we’ll graph the systems we solved in Chap. 27 to see how they work in the

realm of real numbers. Real solutions always appear as intersection points between the graphs

of functions. However, when a two-by-two system has non-real complex solutions, those solu-

tions don’t show up as intersections between real-number graphs.

Linear and Quadratic

The first example we worked out in Chap. 27 involved a system of two equations, one linear

and the other quadratic:

2 x−y+ 1 = 0

and

y=x^2 +x− 5

We called x the independent variable, so we rewrote the first equation as a function of x. The

two-function system then became

y= 2 x+ 1

and

y=x^2 +x− 5

First, we tabulate some points

The graphs we’re about to create aren’t meant to be precise. We aren’t trying to pinpoint the real

solutions using the graphs; we’ve already calculated them! The graphs serve only to geometrically

illustrate the functions and their solutions.

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CHAPTER

28 More Two-by-Two Graphs

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