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Simultaneous Equations

Simultaneous Equations. Word problems. Substitution V Elimination . Explain under what circumstances you should use each method Substitution: Use when 1 (or both) of the equations have y (or x) as the subject (or can readily be in this form without introducing fractions)

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Simultaneous Equations

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  1. Simultaneous Equations Word problems

  2. Substitution V Elimination • Explain under what circumstances you should use each method • Substitution: Use when 1 (or both) of the equations have y (or x) as the subject (or can readily be in this form without introducing fractions) • Elimination: Any other time than above – Note best to put both equations in the form ax + by = c first

  3. Review • Solve y = 2x +1 and y = 5 – 2x using the substitution method • Solution: x = 1, y = 3  (1,3) • Solve 2x + 3y = -1 and 3x – 5y = 8 using the elimination method • Solution: x = 1, y= -1  (1,-1)

  4. Word problems • One of he hardest part is working out what the variables (unknowns) in the question are and defining the variables. • Usually the hint is looking at what you are asked to find these will be your variables • Initially these are given, but you will eventually be required to do this for yourself • Example: The cost of 2 sandwiches and 3 cans of drink is $8.50, while the cost of 3 sandwiches and 5 drinks is $13.50. Find the cost of 1 can of drink and 1 sandwich? • Step 1: What are the variables in this question? Define them! • Let x = Cost of a sandwich, y = cost of a can of drink • How many variable are there in this problem? How many equations will you need to find them? • Step 2: Write 2 equations for this situation • 2x + 3y = 8.50 and 3x + 5y = 13.50 • Step 3: Decide what method you will use to solve them simultaneously • Elimination • Step 3 (con’td): Go and solve • x = 2, y = 1.5 • Step 4: State the solution • A sandwich costs $2 and a can of drink costs $1.50

  5. Try this one The denominator of a fraction is 5 more than the numerator. The sum of the numerator and denominator is 21. What is the fraction? • Define the variables • x = the dominator, y = the numerator • Step 2: Write the equations • x = y + 5 and x + y = 21 • Step 3: Solve the equations: Which method ? • Substitution, x = 13, y = 8 • Step 4: Answer the question • The fraction is 8/13

  6. Try this one • The sum of the ages of 2 bothers, Tom and harry is 32 months. One month ago Harry was four time as old as Tom. How old are they now? • Step 1: Define variables • Let x = Tom’s age now and y = Harry’s age now • Step 2: Write the equations • x + y = 32 and y - 1 = 4 (x – 1) • Step 3: Solve the equations (note you will need to simplify first). What method? • x + y = 32 and y = 4x -3……use substitution • x = 7 and y = 25 • Step 4: State the solution • Tom is 7 months and Harry is 25 months

  7. Harder: Try this one • In AFL football, a goal scores 6 points and a behind scores 1 point. If St Kilda defeated the West Coast Eagles by 104 points to 97 and St Kilda scored the same number of goals as West Coast but scored twice as many behinds, how many goals and behinds did each team score.? • Define the variables • Write the equations • Solve the equations (Choose a method) • State the solution • Let x = No of goals scored by Eagles and y = No of behinds scored by the Eagles • 6x + y = 97 and 6x + 2y = 104 • x = 15, y = 7 • Eagles scored 15 goals 7 behinds and St Kilda scores 15 goals 14 behinds

  8. Try this one! • Quick Couriers charge a $5 pick up fee and 50 cents per km of delivery. Fast Couriers charge $6 pick up and 40 cents per km of delivery. Find the distance which will be same cost for both companies. • Step 1: Define variables: • Let d = distance of delivery and C = Cost of the delivery • Step 2: Write the equations: • C = 5 + 0.5d and C = 6 + 0.4d • Step 3: Solve • Using substitution  d = 10 and C = 10 • Step 4: Answer the Question • For a trip of 10km the cost of both companies is the same.

  9. ..and the last 1 • A rhombus has an area of 50cm. If the slant sides are at an angle of 60 degrees to the base, determine the length each side of the rhombus..

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