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Name: _______________________________ Period: ________ Advanced Algebra 2 – Assignment Sheet Chapter 3: Linear Systems and Matrices HOMEWORK Date Section/Reading Problem Sets 1. 2. 3. 3.1 Pages 153 – 155 3.1 Pages 152 & 159 3.2 Pages 160 – 163 4. 3.1 – 3.2 5. Quiz 3.1 – 3.2 6. 7. 3.3 Pages 168 – 170 3.4 Pages 178 – 181 Pages 156 – 157; #17, 19, 20, 22, 23, 27, 28, 33, 35, 36 Page 152; #1 – 6 and Page 159; #1 – 8 Pages 164 – 165; #4, 5, 7, 10, 16, 18, 22, 23, 28, 31, 36, 39, 41, 43, 55, 56 Extra Practice 3.1 – 3.2 Read Section 3.3 on pages 168 – 170 and complete Guided Practice problems 1, 3 and 4 Pages 171 – 172; #4, 8, 12, 13, 15, 21, 24, 25, 29, 30 Page 183; #25 – 30 Pages 183 – 185; #31, 32, 33, 35, 42 8. 3.4 9. 3.1 – 3.4 Page 1012; #1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14 10. 3.1 – 3.4 Extra Practice 3.1 – 3.4. 11. Study Chapter 3 12. Chapter 3 Test Advanced Algebra 2 Name _________________________ Date ______________ Period _____ 3.1 – Solve Linear Systems by Graphing – Day 1 System of two linear equations Example 1: Graph the system of linear equations and estimate the solution. Then check the solution algebraically. 4x y 8 2 x 3 y 18 Classifying Systems – Example 2: Solve each system by graphing and classify it as consistent and independent, consistent and dependent or inconsistent. a) b) 2 x 5 y 10 4 x 10 y 20 3x 2 y 4 6 x 4 y 12 HW: Pages 156 – 157; #17, 19, 20, 22, 23, 27, 28, 33, 35, 36 Advanced Algebra 2 Name _________________________ Pages 156 – 157; #17, 19, 20, 22, 23, 27, 28, 33, 35, 36 Date ______________ Period _____ 17) 19) 20) 22) 23) 27) 28) 33) 35) 36) Advanced Algebra 2 Name _________________________ Date ______________ Period _____ 3.1 – Solve Linear Systems by Graphing – Day 2 The graphing calculator can be used to solve systems of linear equations. Be sure the equations in the system are in slope-intercept form (solved for y). Press Press and enter the two equations into the calculator. and then press to see the table. Use the arrow buttons to scroll up and down the table until the two y values are the same. The x and y values of the point are the values where the tables match. Another way to use the calculator to solve a system is by graphing both equations on the claculator and finding the point of intersection. Be sure the equations in the system are in slope-intercept form (solved for y). Press Press and enter the two equations into the calculator. to graph the equations. Adjust the window using the Press and then button until the point where the lines intersect is on the screen. to open the calculate menu. Select intersect (#5) from the menu and press enter. Press enter at each of the three prompts. The calculator will position the cursor at the point of intersection and display the x and y coordinates for the solution. Advanced Algebra 2 Name _________________________ Page 152; #1 – 6 and Page 159; #1 – 8 Date ______________ Period _____ 1) 2) 3) 4) 5) 6) Pages 159; #1 – 8 1) 2) 3) 4) 5) 6) 7) 8) Advanced Algebra 2 Name _________________________ Date ______________ Period _____ 3.2 – Solve Linear Systems Algebraically – Day 1 Substitution Method 1) Solve either equation for either variable. 2) Substitute the entire expression for the variable in the opposite equation and solve for the remaining variable. 3) Substitute the value found in step two into either of the original equations and solve for the other variable. Example 1: Solve the system using the substitution method. Remember to check the solution. 4x y 8 2 x 3 y 18 Elimination or Linear Combination Method 1) Multiply one or both equations by a constant to get opposite coefficients for either variable.. 2) Add the revised equations to eliminate one variable and solve for the remaining variable. 3) Substitute the value found in step two into either of the original equations and solve for the other variable. Example 2: Solve the system using the elimination method. 2 x 5 y 11 3x 2 y 7 Example 3: Solve using either method. 2 x 5 y 10 4 x 10 y 20 Example 4: Solve using either method. x 2y 4 2 x 4 y 12 Example 5: Find the coordinates of the point where the diagonals of the quadrilateral intersect. HW: Pages 164 – 165; #4, 5, 7, 10, 16, 18, 22, 23, 28, 31, 36, 39, 41, 43, 55, 56 Advanced Algebra 2 Name _________________________ Pages 164 – 165; Date ______________ Period _____ #4, 5, 7, 10, 16, 18, 22, 23, 28, 31, 36, 39, 41, 43, 55, 56 4) 5) 7) 10) 16) 18) 22) 23) 28) 31) 36) 39) 41) 43) 55) 56) Advanced Algebra 2 Name _________________________ Extra Practice 3.1 – 3.2 – Page 167: 1 – 12 Date ______________ Period _____ 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) Advanced Algebra 2 Name _________________________ Guided Practice 1, 3, & 4 Date ______________ Period _____ 1) 3) 4) Advanced Algebra 2 Name _________________________ Date ______________ Period _____ 3.3 – Graph Systems of Linear Inequalities – Day 1 System of Linear Inequalities – Graphing a System of Linear Inequalities 1) ______________________________________________________________________________ ______________________________________________________________________________ 2) ______________________________________________________________________________ ______________________________________________________________________________ Example 1: Graph the system of inequalities. x y 3 6 x y 1 x 3 Example 2: Graph the system of inequalities. y 7 4 x 5 y 20 Example 3: Graph the system of inequalities. y 2 y x2 HW: Pages 171 – 172; #4, 8, 12, 13, 15, 21, 24, 25, 29, 30. Advanced Algebra 2 Name _________________________ Pages 171 – 172; #4, 8, 12, 13, 15, 21, 24, 25, 29, 30 Date ______________ Period _____ 4) 8) 12) 13) 15) 21) 24) 25) 29) 30) Advanced Algebra 2 Name _________________________ Date ______________ Period _____ 3.4 – Solving Systems of Linear Equations in Three Variables – Day 1 Linear Equation in Three Variables – SOLVING A SYSTEM OF LINEAR EQUATIONS IN THREE VARIABLES 1) Choose two of the equations 2) Apply the linear combination method to eliminate any one of the variables. 3) Choose two of the original equations but not the same two used in Step 2. 4) Apply the linear combination method to eliminate the same variable as in Step 3. 5) Apply the linear combination to the equations from steps 3 and 5 to eliminate either of the variables. 6) Solve for the remaining variable. 7) Substitute into the equation from step 3 or 5 to get the value of the second variable. 8) Use any original equation to solve for the third variable. 9) Write the answer as an ordered triple. Example 1: Solve the system using the elimination method. x yz 2 2x 2 y 2z 6 5 x y 3z 8 Example 2: Solve the system using the elimination method. 3 x y 2 z 10 6 x 2 y z 2 x 4 y 3z 7 Example 3: Solve the system using the elimination method. x yz 3 x yz 3 2x 2 y z 6 Reminders: If any equation has a variable with a coefficient of 1, multiply this equation to eliminate the variable from the other two equations. Double check each multiplication and check that all the signs are correct. Follow the pattern shown in the examples. There can be no solution, infinitely many solutions or exactly one solution written as an ordered triple. Always check the solution in each of the equations. HW: Page 183: #25 – 30 Advanced Algebra 2 Name _________________________ Page 183; #25 – 30 Date ______________ Period _____ 25) 26) 27) 28) 29) 30) Advanced Algebra 2 Name _________________________ Date ______________ Period _____ 3.4 – Solving Systems of Linear Equations in Three Variables – Day 2 Warm Up: Solve the system using the elimination method. x 3y 7 2 x 6 y 4 Solve the system using substitution. x 4 y 4 3x 2 y 5 Example 1 At the snack bar at a football game one hot dog, one pretzel and one soda costs $5.00. Two hot dogs, one pretzel and two sodas costs $8.50 and three hot dogs, one pretzel and two sodas costs $10.75. How much did each item cost individually? SOLVING A SYSTEM OF LINEAR EQUATIONS IN THREE VARIABLES 1) Choose two of the equations 2) Apply the linear combination method to eliminate any one of the variables. 3) Choose two of the original equations but not the same two used in Step 2. 4) Apply the linear combination method to eliminate the same variable as in Step 3. 5) Apply the linear combination to the equations from steps 3 and 5 to eliminate either of the variables. 6) Solve for the remaining variable. 7) Substitute into the equation from step 3 or 5 to get the value of the second variable. 8) Use any original equation to solve for the third variable. 9) Write the answer as an ordered triple. Reminders: If any equation has a variable with a coefficient of 1, multiply this equation to eliminate the variable from the other two equations. Double check each multiplication and check that all the signs are correct. There can be no solution, infinitely many solutions or exactly one solution expressed as an ordered triple. Always check the ordered pair in each of the equations. HW: Pages 183 – 184: 31, 32, 33, 35, 42 Advanced Algebra 2 Name _________________________ Page 183; #31, 32, 33, 35, 42 Date ______________ Period _____ 31) 32) 33) 35) 42) Advanced Algebra 2 Name _________________________ Page 1012; #1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14 Date ______________ Period _____ 1) 2) 4) 5) 6) 7) 8) 10) 11) 12) 13) 14) Advanced Algebra 2 Name _________________________ Extra Practice 3.1 – 3.4 Date ______________ Period _____ 1) Solve the system by graphing. x 2 y 4 3x y 3 2) Solve the system by graphing. 3x 6 y 12 x 2 y 3 3) Solve the system algebraically. 3x 2 y 2 4x 3y 5 4) Solve the system algebraically. 4 x 12 y 36 x 3y 9 5) Graph the system of inequalities 2x y 5 y 2 x 1 6) Graph the system of inequalities 1 y x2 3 y 3x 3 x 1 Solve the system. 3 x y z 2 7) 2 x y 2 z 12 4x 2 y z 1 8) At a snack booth, one soda, one pretzel, and two hot dogs cost $7; two sodas, one pretzel, and two hot dogs cost $8; and one soda and four hot dogs cost $10. What is the price (in dollars) of one hot dog?