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Chapter 4 Section 3

Chapter 4 Section 3. Solving Systems of Equations in two Variables Using Elimination. The Elimination Method. Given a system of two equations in the variables x and y. Rewrite each equation in the form Ax+By=C

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Chapter 4 Section 3

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  1. Chapter 4 Section 3 Solving Systems of Equations in two Variables Using Elimination

  2. The Elimination Method • Given a system of two equations in the variables x and y. • Rewrite each equation in the form Ax+By=C • Add a multiple of one equation to the other equation so that one of the variables is eliminated. • Solve the resulting equation for the variable. • Go back to one of the original equations and use this value to solve for the other variable. • Check the solution.

  3. Problem Solving • Analyze the problem. • Define your variables and form a system of equations. • Solve the system. • Check the solution. • State the conclusion.

  4. Modeling the Real World • A standard tennis court used for doubles has a perimeter of 228ft. The width is given to be 42ft less than the width. Translate into a system of equations.

  5. Green Diamond Can either convert logs into lumber or plywood. In a given day the mill turns out 42 units of plywood and lumber. It makes a profit of $2500 on a unit of lumber and $4000 on a unit of plywood. How many units of each type were produced if they sold all 42 units and made a profit of $124,500?

  6. Example For every problem answered correctly on an exam, 3 points are awarded. For every incorrect answer, 4 point are deducted. In a 10 question test, a student scored 16 points. How many correct and incorrect answers did the student have on the exam.

  7. Example A part-time mover’s regular pay rate is $6 per hour. If the work involves going up and down stairs, his rate increases to $9 per hour. In one week he earned $138 and worked 20 hours. How many hours did he work at each rate?

  8. Mixture Problems Sunflower seed costs $1.00 per pound. Rolled oats cost $1.35 per pound. How many pounds of each seed would you need to make 50 lbs of a mixture that costs $1.14 per pound?

  9. A problem from ancient China (Jiuzhang Suanshu) One pint of good wine costs 50 gold pieces, while one pint of poor wine costs 10. If two pints of wine are bought for 30 gold pieces, how much of each kind of wine was bought?

  10. Example A caterer needs to provide 10 lbs of mixed nuts for a wedding reception. Peanuts cost $2.50 per pound and fancy nuts cost $7.00 per pound. If $40 has been budgeted for nuts, how many pounds of each can be used?

  11. Example A collection of dimes and quarters is worth $15.25. There are 103 coins in all. How many dimes and how many quarters are there?

  12. Example A solution containing 28% fungicide is to be mixed with a solution containing 40% fungicide to make 300 liters of a solution containing 36% fungicide. How much of each solution is needed?

  13. Example A jeweler wishes to make a 60 oz mixture that is two-thirds pure gold. She has two stocks of gold alloy, the first stock contains three-fourths pure gold and the second stock is five-twelfths pure gold. How many ounces of each stock does she need?

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