CHAPTER_ppt_4_5 - 4.5 Systems of Linear Equations and...

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§ 4.5 Systems of Linear Equations and Problem Solving
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Steps in Solving Problems 1) Understand the problem. Read and reread the problem. Choose a variable to represent the unknown. Construct a drawing, whenever possible. Propose a solution and check. 1) Translate the problem into two equations. 2) Solve the system of equations. 3) Interpret the results. Check proposed solution in the problem. State your conclusion. Problem Solving Steps
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Finding an Unknown Number Continued One number is 4 more than twice the second number. Their total is 25. Find the numbers. Read and reread the problem. Suppose that the second number is 5. Then the first number, which is 4 more than twice the second number, would have to be 14 (4 + 2•5). Is their total 25? No: 14 + 5 = 19. Our proposed solution is incorrect, but we now have a better understanding of the problem. Since we are looking for two numbers, we let x = first number y = second number 1.) Understand Example :
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Continued 2.) Translate Finding an Unknown Number x = 4 + 2 y x + y = 25 Example continued :
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 3.) Solve Continued Finding an Unknown Number Using the substitution method, we substitute the solution for x from the first equation into the second equation. x + y = 25 (4 + 2 y ) + y = 25 Replace x with result from first equation. 4 + 3 y = 25 Simplify left side. 3 y = 21 Subtract 4 from both sides and simplify. y = 7 Divide both sides by 3. Now we substitute the value for y into the first equation. x = 4 + 2 y = 4 + 2(7) = 4 + 14 = 18 We are solving the system x = 4 + 2 y and x + y = 25 Example continued :
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 6 4.) Interpret Finding an Unknown Number Check: Substitute x = 18 and y = 7 into both of the equations. First equation, x = 4 + 2 y 18 = 4 + 2( 7 ) true Second equation, x + y = 25 18 + 7 = 25 true State: The two numbers are 18 and 7. Example continued :
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Martin-Gay, Beginning and Intermediate Algebra, 4ed 7 Solving a Problem about Prices Continued Hilton University Drama club sold 311 tickets for a play. Student tickets cost 50 cents each; non-student tickets cost
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CHAPTER_ppt_4_5 - 4.5 Systems of Linear Equations and...

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