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Solving A System of Equations

Solving A System of Equations. Joseph Mares and Cesar Moreno December 19, 2013 5B. Problem Situation.

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Solving A System of Equations

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  1. Solving A System of Equations Joseph Mares and Cesar Moreno December 19, 2013 5B

  2. Problem Situation • An auto mechanic charges a fixed fee for examining a vehicle for engine problems plus an hourly rate for repairing the engine. The mechanic worked for 6 hours on a car with engine problems and the bill totaled $170. The mechanic worked on another car with engine problems for 4 hours, and the bill totaled $130. • Find the fixed fee and the hourly rate.

  3. Define Variables • F is the fixed rate fee, and x is the hourly rate.

  4. System of Equations • F + 6x = $170 • F + 4x= $130

  5. Solution Method • We are going to solve it by elimination.

  6. Steps of Solution • F + 6x = $170 Eliminate the F by subtracting F + 4x= $130 the equations. • 2x = $ 40 • Divide both sides by 2. • x = $ 20 • Use 20 in the first equation. • F + 6(20) = 170 Multiply and then subtract. • F + 120 = 170 F = 50

  7. Solution to the System of Equations (50,20)

  8. Check of Solution • 50 + 4*20 = 130 ☺ • 50 + 6*20 = 170 ☺

  9. Solution in the Problem Situation • $50 is the fixed rate fee and $20is the hourly rate.

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