STUDY SKILLS
Your textbook provides material to help you prepare for quizzes or tests in this course.
Refer to a Chapter Summaryas you read through the following techniques.
Chapter Reviewing Techniques
N Review the Key Terms.Make a study card for each. Include
a definition, an example, a sketch (if appropriate), and a
section or page reference.
N Take the Test Your Word Power quizto check your under-
standing of new vocabulary. The answers immediately
follow.
N Read the Quick Review.Pay special attention to the head-
ings. Study the explanations and examples given for each
concept. Try to think about the whole chapter.
N Reread your lecture notes.Focus on what your instructor
has emphasized in class, and review that material in your
text.
N Work the Review Exercises.They are grouped by section.
✓Pay attention to direction words, such as simplify,
solve, and estimate.
✓After you’ve done each section of exercises, check
your answers in the answer section.
✓Are your answers exact and complete? Did you in-
clude the correct labels, such as $, cm^2 , ft, etc.?
✓Make study cards for difficult problems.
N Work the Mixed Review Exercises.They are in mixed-
up order. Check your answers in the answer section.
N Take the Chapter Test under test conditions.
✓Time yourself.
✓Use a calculator or notes (if your instructor permits them on tests).
✓Take the test in one sitting.
✓Show all your work.
✓Check your answers in the back of the book. Section references are provided.Reviewing a chapter will take some time.Avoid rushing through your review in one
night. Use the suggestions over a few days or evenings to better understand the mate-
rial and remember it longer.
Follow these reviewing techniques for your next test. Evaluate how they worked
for you.
Reviewing a Chapter
system of linear equations4.1
(linear system)
solution set of a systemsolution of a system
set-builder notationconsistent systeminconsistent systemindependent equations
dependent equations system of linear inequalitiessolution set of a system of4.5
linear inequalitiesKEY TERMS1.A system of linear equations
consists ofA.at least two linear equations with
B.different variablestwo or more linear equations that
have an infinite number ofsolutions
C.two or more linear equationswith the same variables
D.two or more linear inequalities.2.A consistent systemis a system of
equationsA.with one solution
C.B.with an infinite number ofwith no solution
D.solutionsthat have the same graph.
3.An inconsistent systemis a system
of equationsA.with one solution
B.with no solutionC.with an infinite number of
D.solutionsthat have the same graph.- Dependent equationsA.have different graphs
B.C.have no solutionhave one solution
D.are different forms of the sameequation.
TEST YOUR WORD POWER
See how well you have learned the vocabulary in this chapter.4.1Solving Systems of Linear Equations
by Graphing
An ordered pair is a solution of a system if it makes allequations of the system true at the same time.To solve a linear system by graphing, follow these steps.
Step 1Graph each equation of the system on the same
axes.
Step 2 Find the coordinates of the point of intersection.
Step 3Check. Write the solution set.Is a solution of the following system?
Yes, because and are both true,
is a solution.
Solve the system by graphing.The solution is the solution set. 1 3, 2 2 checks, so (^51) 3, 2 26
x+y= 5
2 x-y= 4
1 4, - 12 4 +^1 -^12 =^32142 -^1 -^12 =^9
x+y= 3
2 x-y= 9
1 4, - 12
QUICK REVIEW
CONCEPTS EXAMPLES
ANSWERS
SUMMARY
CHAPTER 4
1.C; Example: 2.A; Example:The system in
one point—in this case, the solution intersect, so there is no solution to the system.3.B; Example:The equations of two parallel lines make up an inconsistent system. Their graphs neverAnswer 1is consistent. The graphs of the equations intersect at exactly
the same line.^1 2, 3^2. 4.D; Example:The equations 4 x-y= (^8) and 8 x- 2 y= 16 are dependent because their graphs are
2 x+y=7, 3 x-y= 3
x
y
0
5
–4
2 5
(3, 2) x + y = 5
2 x – y = 4
(continued)
(^286) CHAPTER 4Systems of Linear Equations and Inequalities