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In Chapter 3, you will apply the big ideas listed below and reviewed in the Chapter Summary on page 221. You will also use the key vocabulary listed below. Big Ideas 1 Solving systems of equations using a variety of methods 2 Graphing systems of equations and inequalities 3 Using matrices KEY VOCABULARY • system of two linear equations, p. 153 • consistent, p. 154 • inconsistent, p. 154 • independent, p. 154 • dependent, p. 154 • substitution method, p. 160 • elimination method, p. 161 • system of linear inequalities, p. 168 • system of three linear equations, p. 178 Other animations for Chapter 3: pages 161, 168, 196, and 211 • ordered triple, p. 178 • matrix, p. 187 • determinant, p. 203 • Cramer’s rule, p. 205 • identity matrix, p. 210 • inverse matrices, p. 210 You can use systems of linear equations to solve real-world problems. For example, you can determine which of two payment options for riding a bus is more cost-effective. Algebra The animation illustrated below for Example 4 on page 155 helps you answer this question: After how many bus rides will the cost of two payment options be the same? You want to decide whether to pay for bus rides individually or buy a monthly pass. Algebra at classzone.com Now Why? �� Enter linear equations to compare the costs of the two payment options. 151
Investigating g g Algebra 3.1 Solving Linear Systems Using Tables MATERIALS • graphing calculator QUESTION How can you solve a system of linear equations using a table? An example of a system of linear equations in two variables x and y is the following: y 5 2x 1 4 Equation 1 y 523x 1 44 Equation 2 A solution of a system of equations in two variables is an ordered pair (x, y) that is a solution of both equations. One way to solve a system is to use the table feature of a graphing calculator. E XPLORE Solve a system Use a table to solve the system of equations above. STEP 1 Enter equations Press to enter the equations. Enter Equation 1 as y 1 and Equation 2 as y 2 . Y1=2X+4 Y2=-3X+44 Y3= Y4= Y5= Y6= Y7= ACTIVITY c The solution of the system is (8, 20). DRAW CONCLUSIONS Use your observations to complete these exercises Use a table to solve the system. If you are using a graphing calculator, you may need to first solve the equations in the system for y before entering them. 1. y 5 2x 1 5 2. y 5 4x 1 1 3. y 5 4x 2 3 y 52x 1 2 y 5 4x 2 8 y 5 3 } 2 x 1 2 4. 8x 2 4y 5 16 5. 6x 2 2y 522 6. x 1 y 5 11 26x 1 3y 5 3 23x 2 7y 5 17 2x 2 y 5211 7. Based on your results in Exercises 1–6, make a conjecture about the number of solutions a system of linear equations can have. 152 Chapter 3 Linear Systems and Matrices STEP 2 Make a table Set the starting x-value of the table to 0 and the step value to 1. Then use the table feature to make a table. X 0 1 2 3 4 X=0 Y1 4 6 8 10 12 Use before Lesson 3.1 Y2 44 41 38 35 32 STEP 3 Find the solution Scroll through the table until you find an x-value for which y 1 and y 2 are equal. The table shows y 1 5 y 2 5 20 when x 5 8. X 4 5 6 7 8 X=8 TEXAS classzone.com Keystrokes Y1 12 14 16 18 20 TEKS Y2 32 29 26 23 20 a.5, a.6, 2A.3.B, 2A.3.C
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