Math141HW5F11Shortened

# Math141HW5F11Shortened - (Exercises for Chapter 7 Systems...

This preview shows pages 1–5. Sign up to view the full content.

(Exercises for Chapter 7: Systems and Inequalities) E.7.1 CHAPTER 7: Systems and Inequalities (A) means “refer to Part A,” (B) means “refer to Part B,” etc. (Calculator) means “use a calculator.” Otherwise, do not use a calculator. SECTIONS 7.1-7.3: SYSTEMS OF EQUATIONS When solving a system, only give solutions in ± 2 , the set of ordered pairs of real numbers. All such solutions correspond to intersection points of the graphs of the given equations. If there are no such solutions, write ± , the empty set or null set. Write solutions in a solution set as ordered pairs of the form x , y () . Unless otherwise specified, do not rely on graphing or “trial-and-error point-plotting.” 1) Consider the system x + y = 5 5 x ± 3 y = ± 23 ² ³ ´ . (A-E) a) The graphs of the equations in the system are distinct lines in the xy -plane that are not parallel. How many solutions does this system have? b) Solve the system using the Substitution Method. c) Solve the system using the Addition / Elimination Method. 2) Consider the system x 2 + y 2 = 2 y = x + 2 ± ² ³ . (A-D) a) Find the solution set of the system. b) Use the solution set from a) to graph the equations in the system in the usual xy -plane. 3) Consider the system x 2 + y 2 = 3 2 y 2 = x 2 ± ² ³ ´ ³ . (A-D) a) What are the graphs of the equations in the system in the usual xy -plane? b) How many solutions does the system have? c) Find the solution set of the system.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(Exercises for Chapter 7: Systems and Inequalities) E.7.2 4) Consider the system x = y 2 x = 4 ± y 2 ² ³ ´ µ ´ . (A-D; Section 1.8) a) What are the graphs of the equations in the system in the usual xy -plane? b) How many solutions does the system have? c) Find the solution set of the system. 5) Consider the system x 2 + y = 0 y ± x 2 = 1 ² ³ ´ µ ´ . (A-D, F) a) Sketch graphs of the equations in the system in the usual xy -plane. b) Based on your graphs in a), find the solution set of the system. c) Verify the solution set by using the Substitution Method or the Addition / Elimination Method to solve the system. 6) Solve the following systems. (A-D, F) a) y = 3 x 2 ± x y = 2 x 2 ± 3 x + 8 ² ³ ´ µ ´ b) x 2 + 4 y 2 = 2 3 x ± 2 y = ± 4 ² ³ ´ c) x 2 + y 2 = 1 x 2 ± y 2 = 4 ² ³ ´ µ ´ 7) ADDITIONAL PROBLEM. Solve the system 0 = 0 0 = 1 ± ² ³ . (A-D, F)
(Exercises for Chapter 7: Systems and Inequalities) E.7.3 SECTION 7.4: PARTIAL FRACTIONS 1) Write the PFD (Partial Fraction Decomposition) Form for the following. Do not find the unknowns ( A , B , etc.). (A-C) a) 1 x + 4 () x ± 3 x 2 + 1 b) x + 5 x 3 x ± 1 2 x 2 + 3 2 c) 3 t 2 + 2 t ± 2 t 2 2 t + 5 3 2 t 2 + 5 t 2 + t + 1 2) Write the PFD (Partial Fraction Decomposition) for the following. (A-G) a) 3 x ± 5 x 2 ± 5 x + 6 b) 2 x 2 ± 3 x + 19 x 3 + 4 x 2 ± 7 x ± 10 . (Hint: Use the Rational Zero Test and Synthetic Division.) c) 9 x 2 + 14 x + 6 2 x 3 + x 2 d) x + 1 x 2 ± 8 x + 16 e) 8 x 2 + 7 x + 12 x + 2 x 2 + 1 f) 5 x 2 ± 5 x + 12 x 3 ± 5 x 2 + 3 x ± 15 . (Hint: Use Factoring by Grouping.) g) ± 5 x 2 ± 8 x ± 3 x 3 + x 2 + x h) 5 t 3 ± t 2 + 20 t ± 8 t 2 + 4 2 3) A student writes: x 4 x + 3 x + 5 = A x + 3 + B x + 5 . Is this appropriate? Why or why not?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(Exercises for Chapter 8: Matrices and Determinants) E.8.1 CHAPTER 8:
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 22

Math141HW5F11Shortened - (Exercises for Chapter 7 Systems...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online