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Name ________________________________________ Date __________________ Class __________________ LESSON 12-1 Creating Systems of Linear Equations Practice and Problem Solving: A/B Write and solve a system of equations for each situation. 1. One week Beth bought 3 apples and 8 pears for $14.50. The next week she bought 6 apples and 4 pears and paid $14. Find the cost of 1 apple and the cost of 1 pear. _________________________________________________________________________________________ 2. Brian bought beverages for his coworkers. One day he bought 3 lemonades and 4 iced teas for $12.00. The next day he bought 5 lemonades and 2 iced teas for $11.50. Find the cost of 1 lemonade and 1 iced tea, to the nearest cent. _________________________________________________________________________________________ Two campgrounds rent a campsite for one night according to the following table. Use the table for 3–5. Number of campers Sunnyside Campground Green Mountain Campground 1 2 3 4 $58 $66 $74 $82 $40 $50 $60 $70 3. Write the equation for the rate charged by Sunnyside Campground. _________________________________________________________________________________________ 4. Write the equation for the rate charged by Green Mountain. _________________________________________________________________________________________ 5. Solve the system of the equations you found in Problems 3 and 4. For how many campers do the campgrounds charge the same rate? What is the rate charged for that number of campers? _________________________________________________________________________________________ Use the graph for 6–8. 6. Write the functions represented by the graph. 7. What does each function represent? What does the variable represent? _____________________________________________________ 8. Solve the system of equations. Is the intersection point shown on the graph correct? ____________________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 202 2. 4 x + y + 2z = 10 Practice and Problem Solving: Modified −( x + y − 6z = −23.5) 1. 2nd; 3 or −3 2 x + 3 y + 3z = 13 −3( x + y − 6z = −23.5) 3 x + 8z = 33.5 − x + 21z = 83.5 st 2. 1 ; 2 or −2 3 x + 8z = 33.5 3. 1st; 4 or −4 x = 0.5 + 3( − x + 21z = 84.5) 4. 2nd; 4 or −4 71z = 284 z=4 5. (2, 3) 6. (−6, 4) 7. (4, −1) x + y − 6z = −23.5 8. (2, 0) 0.5 + y − 6(4) = −23.5 y =0 9. One hot chocolate is $1. 10. 9 two-point shots and 3 three-point shots MODULE 12 Modeling with Linear Systems 1. Multiply the first equation by 3 and the second equation by 5 to get common coefficients of −15. LESSON 12-1 ⎧ 4(9x − 10y = 7) ⎧36x − 40y = 28 2. ⎨ ⇒⎨ ⎩5(5x + 8y = 31) ⎩25x + 40y = 155 3. (1, −3) Practice and Problem Solving: A/B 1. apple: $1.50, pear $1.25 4. (10, −10) 2. lemonade: $1.57, iced tea: $1.82 Success for English Learners 3. y = 8x + 50 1. The y-variable is eliminated. 4. y = 10x + 30 2. Multiply the equation by −3 so that the y-variable is eliminated. 5. The camp grounds will both charge $130 for 10 campers. 6. g(t) = 2t + 4, h(t) = 2.5t + 2 MODULE 11 Challenge x + y + z = 12 +(3 x + y − z = 32) 4 x + 2y = 44 4 x + 2y = 44 −(6 x + 2y = 56) 7. The functions represent the rates charged by 2 different dog walkers. The variable represents the number of dogs. 3 x + y − z = 32 +(3 x + y + z = 24) 6 x + 2y = 56 8. Yes Practice and Problem Solving: C 4(6) + 2y = 44 y = 10 1. y = − 2 x = −12 1 x 2 2. Sample answer: The number of bales of hay needed to feed 3 elephants. x=6 6 + 10 + z = 12 Solution: (0.5, 0, 4) The solution checks in all three equations. Reading Strategies 1. 3 x + 8(4) = 33.5 3. Sample answer: Let x = number of bales of hay; Let y = the number of elephants; 1 + 1, y = x − 3 (6, 3); y = 3x Solution: (6, 10, −4) z = −4 The solution checks in all three equations. Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 547