Intermediate Algebra (11th edition)

38.Repeat Exercise 37for the graph of , shown in the figure.

y^2 9

x^2 = 1

SECTION 11.4 Nonlinear Systems of Equations 657

TECHNOLOGY INSIGHTS EXERCISES 37 AND 38

37.The hyperbola shown in the figure was graphed in function mode, with a square viewing window. It

is the graph of. What are the two functions and that were used to obtain this graph?

y 1 y 2

x^2 9

y^2 = 1

10

–10

–15 15

10

–10

–15 15

Use a graphing calculator in function mode to graph each hyperbola. Use a square viewing window.

Solve each system. See Section 4.1.

PREVIEW EXERCISES

y^2 - 9 x^2 = 9 y^2 - 9 x^2 = 36

x^2 4

-

y^2 16

= 1

x^2 25

-

y^2 49

= 1

43. 44. 45. 46.

10 x- 3 y= 46

5 x+ 7 y= 6 4 x+ 6 y= 8

4 x- 3 y=- 10 x- y=- 5

9 x+ 2 y= 10 y= 3 x+ 3

2 x+y= 13

Solve each equation. See Section 9.3.

2 x^4 - 5 x^2 - 3 = 0 48.x^4 - 7 x^2 + 12 = 0

OBJECTIVES An equation in which some terms have more than one variable or a variable of degree 2

or greater is called a nonlinear equation.A nonlinear system of equationsincludes at

least one nonlinear equation.

When solving a nonlinear system, it helps to visualize the types of graphs of the

equations of the system to determine the possible number of points of intersection.

For example, if a system includes two equations where the graph of one is a circle and

the graph of the other is a line, then there may be zero, one, or two points of intersec-

tion, as illustrated in FIGURE 26.

Nonlinear Systems of Equations

11.4

1 Solve a nonlinear system by substitution. 2 Solve a nonlinear system by elimination. 3 Solve a nonlinear system that requires a combination of methods. x

y

0

No points of intersection

x

y

0

One point of intersection

x

y

0

Two points of intersection FIGURE 26