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Name ________________________________________ Date __________________ Class __________________ LESSON 8-4 Solving Systems by Elimination with Multiplication Practice and Problem Solving: D Fill in the blanks to solve each system by elimination with multiplication. The first one has been started for you. ⎧3 x + 4 y = 26 1. ⎨ ⎩ x − 2y = −8 Multiply the second equation by 2. Then, add the equations: ⎧⎪ 3 x + 4 y = 26 ⎨ ⎪⎩2 ( x − 2y = −8 ) 3x + 4y = 26 −16 2 4 + ______ x − ______ y = ______ ______ x + 0 = ______ ______ x = ______ ÷ ______ ÷ ______ x = ______ Substitute ______ for x in one of the equations: x − 2y = − 8 ______ − 2y = −8 − ______ − ______ −2y = ______ ÷ ______ ÷ ______ y = ______ Solution: (______, ______) 2. Last month, Stephanie spent $57 on 4 allergy shots and 1 office visit. This month, she spent $9 after 1 office visit and a refund for 2 allergy shots from her insurance company. How much do an allergy shot and an office visit cost? Complete the equations: 4a + 1v = _________ −2a + 1v = _________ Allergy shot: $_________; office visit: $_________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 178 Reading Strategies 8. All of the lines would intersect at (−1, −2) but would have different slopes less than +1 and different y-intercepts. 1. The hand towels are the variable to eliminate. Bath towels: $10; hand towels: $5 9. (−1, 2) 2. The adult movie ticket is the variable to eliminate. Adult tickets: $15; child tickets: $5 10 −11 Answers may vary, but the two systems should have equations of the form nx + (n + 1)y = n + 2 and (n + 3)x + (n + 4) y = (n + 5), where n is an integer; (−1, 2); (−1, 2). Success for English Learners 1. The y-variable is eliminated. −2y + −2y = 0 2. The “2D” in both equations is eliminated, and you get 2L = 16. The lunch combo is $8. Practice and Problem Solving: D 1. 2; 4; −16; 5; 10; 5; 10; 5; 5; 2; 2; 2; 2; 2; −10; −2; −2; 5; 2; 5 LESSON 8-4 2. 57; 9; 8; 25 Practice and Problem Solving: A/B Reteach 1. 4; 6 22 ⎞ ⎛ 59 1. ⎜ , − ⎟ 7 ⎠ ⎝ 7 2. 42; 90 3. 24; 60 111 ⎞ ⎛ 2. ⎜ 69, ⎟ 2 ⎠ ⎝ 29 ⎞ ⎛ 17 4. ⎜ , − ⎟ 5 ⎠ ⎝ 5 5 ⎞ ⎛ 135 3. ⎜ ,− ⎟ 19 ⎠ ⎝ 19 ⎛ 1 ⎞ 5. ⎜ − , 3 ⎟ ⎝ 2 ⎠ ⎛ 27 119 ⎞ 4. ⎜ , − ⎟ 10 ⎠ ⎝ 10 6. (−4, −1) 7. 2a + 3y = 134; 3a + 2y = 146; $22 Reading Strategies 8. x + y = 19; 0.25x + 0.3y = 5.1; 7 Galas, 12 Granny Smith’s 1. Multiply the first equation by 3 and the second equation by 5 to get common coefficients of −15. Practice and Problem Solving: C 1. (−1, −2) 2. (−1, −2) ⎧4(9 x − 10 y = 7) ⎧36 x − 40 y = 28 2. ⎨ ⇒⎨ ⎩5(5 x + 8 y = 31) ⎩25 x + 40 y = 155 3. (−1, −2) 3. (1, −3) 4. The numbers are consecutive whole numbers. 4. (10, −10) Success for English Learners 1. −3 5. (−1, −2). They follow the pattern. 2. Multiply the first equation by 3 and the second by −2, or the first by −3 and the second by 2. 2 4 3 5 x − ; y = x − ; both slopes are 3 3 4 4 close to but less than +1. 6. y = 7. The slopes are getting larger and approaching positive one. Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 362