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Review 3-1 and 3-2 SLIDE SHOW
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Solve the linear system using the substitution method. 3 x + 4y – 4 Equation 1 x + 2y 2 Equation 2 x + 2y 2 x – 2y + 2 3(– 2y + 2) + 4y – 4 y 5y 5 S OLUTION -6y+6+4y – 4 -2y = -10 x – 2y + 2 x – 2(5) + 2 x – 8x – 8 The solution is (– 8, 5). 1.
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x – 2 y 3 2 x – 4 y 7 2(2 y + 3) – 4 y 7 6 7 Because the statement 6 = 7 is never true, there is no solution. 2. Solve the linear system using the substitution method. x 2 y + 3
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Solve the linear system using the linear combination/elimination method. 2 x – 4y 13 Equation 1 4 x – 5y 8 Equation 2 – 4x + 8y – 26 4 x – 5y 8 2 x – 4y 13 4 x – 5y 8 3y –18 y – 6y – 6 Multiply the first equation by – 2 so that x -coefficients differ only in sign. S OLUTION – 2 3.
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The Linear Combination Method: Multiplying One Equation 2 x – 4y 13 2 x – 4(– 6) 13 2 x + 24 13 x – 11 2 The solution is –, – 6. (- 5 1 2 ) y – 6y – 6 Add the revised equations and solve for y. Write Equation 1. Substitute – 6 for y. Simplify. Solve for x. Substitute the value of y into one of the original equations. Solve the linear system using the linear combination method. 2 x – 4y 13 Equation 1 4 x – 5y 8 Equation 2
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6 x – 10 y 12 – 15 x + 25 y – 30 Solve the linear system 6 x – 10 y 12 – 15 x + 25 y – 30 30 x – 50 y 60 – 30 x + 50 y – 60 0 0 Add the revised equations. Since no coefficient is 1 or –1, use the linear combination method. Because the equation 0 = 0 is always true, there are infinitely many solutions. S OLUTION 5 2 4.
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7 x – 12 y – 22 Equation 1 – 5 x + 8 y 14 Equation 2 Solve the linear system using the linear combination method. 7 x – 12 y – 22 – 5 x + 8 y 14 14 x – 24y – 44 – 15 x + 24y 42 Add the revised equations and solve for x. – x – 2– x – 2 x 2 Multiply the first equation by 2 and the second equation by 3 so that the coefficients of y differ only in sign. S OLUTION 2 3 5.
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– 5 x + 8 y 14 y = 3 – 5 (2) + 8 y 14 The solution is (2, 3). x 2 Add the revised equations and solve for x. Write Equation 2. Substitute 2 for x. Solve for y. Substitute the value of x into one of the original equations. Solve for y. 7 x – 12 y – 22 Equation 1 – 5 x + 8 y 14 Equation 2 Solve the linear system using the linear combination method. Check the solution algebraically or graphically.
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6. If Brian bought 6 markers and 12 pens for $21.60 and then had to go back and buy 18 more markers and 20 pens for $50.40. How much was each item? 7. If Maria bought 33 books notebooks for $393. Each book costs $23.50 and each notebook costs $2.25. How many of each did she purchase? 6x + 12y = 21.60 18x + 20y = 50.40 x = 1.8 y =.9 Markers costs $1.80 Pens costs $0.90 x + y = 33 23.5x + 2.25y = 393 x = 15 y = 18 15 Books 18 Notebooks
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Homework Textbook Page 155 Quiz 1 1-12 all
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