Page 63

messersmith_power_introductory_algebra_1e_ch4_7_10

Definition/Procedure Example 4.4 Applications of Systems of Two Equations Use the Five Steps for Solving Applied Problems outlined in the section to solve an applied problem. Step 1: Read the problem carefully. Draw a picture, if applicable. Identify what you are being asked to fi nd. Step 2: Choose variables to represent the unknown quantities. If applicable, label the picture with the variables. Step 3: Write a system of equations using two variables. It may be helpful to begin by writing an equation in words. Step 4: Solve the system. Step 5: Check the answer in the original problem, and interpret the solution as it relates to the problem. (p. 274) Amana spent $40.20 at a second-hand movie and music store when she purchased some DVDs and CDs. Each DVD cost $6.30, and each CD cost $2.50. How many DVDs and CDs did she buy if she purchased 10 items all together? Step 1: Read the problem carefully. Step 2: Choose variables. x number of DVDs she bought y number of CDs she bought Step 3: One equation involves the cost of the items: Cost DVDs Cost CDs Total cost 6.30x 2.50y 40.20 The second equation involves the number of items: Number of Number of DVDs CDs Total number of items x y 10 The system is 6.30x 2.50y 40.20. x y 10 Step 4: Multiply by 10 to eliminate the decimals in the fi rst equation, and then solve the system using substitution. 10(6.30x 2.50y) 10(40.20) Eliminate decimals. 63x 25y 402 Solve the system 63x 25y 402 to determine that the x y 10 solution is (4, 6). Step 5: Amana bought 4 DVDs and 6 CDs. Verify the solution. 4.5 Linear Inequalities in Two Variables A linear inequality in two variables is an inequality that can be written in the form Ax By C or Ax By C, where A, B, and C are real numbers and where A and B are not both zero. ( and may be substituted for and .) (p. 286) Graphing a Linear Inequality in Two Variables Using the Test Point Method Step 1: Graph the boundary line. a) If the inequality contains or , make it a solid line. b) If the inequality contains or , make it a dotted line. Step 2: Choose a test point not on the line, and shade the appropriate region. Substitute the test point into the inequality. a) If it makes the inequality true, shade the side of the line containing the test point. All points in the shaded region are part of the solution set. b) If the test point does not satisfy the inequality, shade the other side of the line. All points in the shaded region are part of the solution set. Some examples of linear inequalities in two variables are x 2y 3,   y 1 2 x 4,   y 5,    x 7 Graph using the test point method. 2x y 3 Step 1: Graph the boundary line as a dotted line. Step 2: Choose a test point not on the line, and substitute it into the inequality to determine whether or not it makes the inequality true. Test Point Substitute into 2x y 3 (0, 0) 2(0) (0) 3 0 0 3 0 3 True Since the test point satisfi es the inequality, shade the side of the line containing (0, 0). www.mhhe.com/messersmith CHAPTER 4 Summary 301


messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above