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Writing Systems of Equations

Writing Systems of Equations. Systems of Linear Equations. A system of two linear equations must have 2 variables in both equations. Use variables that represent the quantities they represent.

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Writing Systems of Equations

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  1. Writing Systems of Equations

  2. Systems of Linear Equations • A system of two linear equations must have 2 variables in both equations. • Use variables that represent the quantities they represent. • For example, if you are formulating equations representing the number of cats versus the number of dogs, use the variables “c” and “d.”

  3. Systems of Equations involving COST Blackhills Barbecue Benefit tickets cost $25 for regular tickets and $15 for member tickets. There were 321 total tickets sold. The benefit raised $6935. How many of each type of ticket were sold? • Choose variables that represent the quantities. Use “r” for the number of regular tickets and “m” for the number of member tickets. • One equation should represent the NUMBER of each type of ticket. The other equation should represent the COST of each type of ticket. r + m = 321 25r + 15m = 6935

  4. Systems of Equations involving COST Maggie has 201 coins in her piggy bank. She has $86.90 in dimes and half dollars. How many of each type of coin does Maggie have? • Choose variables that represent the quantities. Use “d” for the number of dimes and “h” for the number of half dollars. • One equation should represent the NUMBER of each type of coin. The other equation should represent the monetary value (COST) of each type of coin. d + h = 201 .10d + .50h = 86.90

  5. Systems of Equations involving COST Your family goes to a Southern-style restaurant for dinner. There are 6 people in your family. Some people order the chicken meal for $14 and some order the steak meal for $17. The total bill was $99. How many people ordered each type of meal?

  6. Systems of Equation involving COST Laura has a coin purse full of nickels and dimes. She has a total of $10.25 in her coin purse. How many of each type of coin does Laura have?

  7. Other Examples of Systems of Equations Naomi took a 40-question history exam. The exam had only multiple-choice and short-answer questions. Each multiple-choice question was worth one point; each short answer question was worth five points; the whole exam was worth 100 points. How many multiple-choice and short-answer questions were on the exam? • Choose variables that represent the quantities. Use “m” for the number of multiple-choice questions and “s” for the number of short-answer questions. • One equation should represent the NUMBER of each type of question. The other equation should represent the POINT VALUE of each type of question. m + s = 40 m + 5s = 100

  8. Other Examples of Systems of Equations There are a total of 50 questions worth 130 points on Mark’s geography exam. Some of the questions are worth five points each, and the other questions are worth two points each. Write a system of equations to determine f, the number of five-point questions, and t, the number of two point questions.

  9. Other Examples of Systems of Equations Joey collects football cards and baseball cards. He has a total of 160 cards. The number of football cards, f, is twelve more than twice the number of baseball cards, b. Write a system of equations that could be used to determine the number of each type of cards Joey has.

  10. Other Examples of Systems of Equations The sum of Ken’s and Alan’s ages is 62. Ken is 32 years older than Alan. Write a system of equations that best describes the age of Ken and Alan.

  11. Other Examples of Systems of Equations Charlie is making a rectangular picture frame. The height of the frame is six inches longer than the width. The perimeter of the frame is 76 inches. Write a system of equations that could be used to solve for the dimensions of the frame.

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