Intermediate Algebra (11th edition)

662 CHAPTER 11 Nonlinear Functions, Conic Sections, and Nonlinear Systems

Complete solution available
on the Video Resources on DVD

11.4 EXERCISES

Concept Check Each sketch represents the graphs of a pair of equations in a system. How

many points are in each solution set?

3. 4.

Concept Check Suppose that a nonlinear system is composed of equations whose graphs

are those described, and the number of points of intersection of the two graphs is as given.

Make a sketch satisfying these conditions. (There may be more than one way to do this.)

5.A line and a circle; no points 6.A line and a circle; one point

7.A line and a hyperbola; one point 8.A line and an ellipse; no points

9.A circle and an ellipse; four points 10.A parabola and an ellipse; one point

11.A parabola and an ellipse; four points 12.A parabola and a hyperbola; two points

Solve each system by the substitution method. See Examples 1 and 2.

x

y

0 x

y

0

x

y

(^0) x
y
0

13. 14.

3 y= 12 x

y=x^2 + 6 x

y=x

y= 4 x^2 - x

15. 16.

x-y=- 4

y=x^2 + 8 x+ 16

x+y= 3

y=x^2 + 6 x+ 9

17. 18.

x= 4 y

2 x^2 + 4 y^2 = 4

2 x+ y= 1

x^2 +y^2 = 2

19. 20.

2 x+y= 3

xy=- 5

3 x+ 2 y=- 10

xy= 4

21. 22.

x+y= 8

xy= 12

x+y=- 2

xy=- 3

23. 24.

y= 5 x^2 + 2 x- 7

y= 2 x^2 + 1

y=x^2 - x- 6

y= 3 x^2 + 6 x

25. 26.

y=x^2 - 2

x^2 +y^2 = 4

y=x^2 - 3

2 x^2 - y^2 = 6

27. 28.

2 x-y= 3

x^2 - 3 x+y^2 = 4

x- 2 y= 1

x^2 - xy+y^2 = 0