Solving Systems of Equations Graphically (Week of JAN 6-9)



Solving Systems of Equations Graphically

Essential Questions:

1. What is a system of equations?

2. What is the solution to a system?

3. How is the solution found graphically?

4. How can a solution be verified algebraically?

For each of the following scenarios:

a. Write a system of linear equations.

b. Graph the system. Use the appropriate scale.

c. Determine the solution to the system and write it as an ordered pair.

d. Verify the solution algebraically by substituting the values into both equations to check that the ordered pair makes a true statement.

1. Wyatt and Jenni are reading the same book. Wyatt is on page 14 and reads 2 pages every night. Jenni is on page 6 and reads 3 pages every night. After how many nights will they have read the same number of pages? How many pages will that be?

2. The school band sells carnations on Valentine’s Day for $2 each. They buy the carnations from a florist for $1 each, plus a $16 delivery charge. What does the solution to this system represent?

3. Angelo runs 7 miles and increases his distance by 1 mile each week. Marc runs 4 miles and increases his distance by 2 miles each week. In how many weeks will Angelo and Marc be running the same distance? What will that distance be?

4. To deliver mulch, Lawn and Garden charges $30 per cubic yard of mulch plus a $30 delivery fee. Yard Depot charges $25 per cubic yard plus a $55 delivery fee. For how many cubic yards will the cost be the same? What will that cost be?

5. The Warrior baseball team is selling hats as a fund-raiser. They contracted two companies. Hats Off charges a $50 design fee and $5 per hat. Top Stuff charges a $25 design fee and $6 per hat. For how many hats will the cost be the same? What is that cost? Explain when it is cheaper for the baseball team to use Top Stuff and when it is cheaper to use Hats Off.

6. Maryann and Carlos are each saving for new scooters. So far, Maryann has $9 saved, and can earn $6 per hour babysitting. Carlos has saved $3, and can earn $9 per hour working at his family’s restaurant. After how many hours of work will Maryann and Carlos have saved the same amount? What will that amount be?

7. The Science Club needs to rent a bus for a field trip. Main Street Buses charges a $40 rental fee, plus $2 per mile. County Bus Line charges a $20 rental fee, plus $3 per mile. For what number of miles will the total charge be the same? What will that charge be?

8. Joy has 5 collectible stamps and will buy 2 more each month. Ronald has 25 collectible stamps and will sell 3 each month. After how many months will they have the same number of stamps? How many will that be?

9. A teacher needs to rent video equipment. 4Rent charges $20 for each hour. Rent It Here charges $80 plus $10 per hour. After how many hours is the cost of renting video equipment the same from both companies?

10. Dawn is having a party catered. Good Eats charges $50 plus $5 per person. Food Fare charges $20 plus $10 per person. Find the number of people for which the total cost is the same for both catering companies. For what size party would you want to use Good Eats? Food Fare?

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