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7.4 Day 2 - Applications
Warm-up:
Solve the linear system using elimination.
1. 8x + 3y = 12
-2x + y = 4
2. -3x + 2y = 7
5x – 4y = -27
3. -7x – 3y = 11
4x – 2y = 16
4. 2x + 3y = -9
x – 2y = 6
x–y=3
6.
x+y=7
1
4
x–
1
4
y=
5
4
1
0.4x + 0.1y = 0.7
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5.
Goal: Write and solve systems of equations using elimination.
Example 1 Fabric Darlene is making a quilt that has alternating stripes of regular quilting fabric
and sateen fabric. She spends $76 on a total of 16 yards of the two fabrics at a fabric store. Which
system of equations can be used to find the amount x (in yards) of regular quilting fabric and the
amount y (in yards) of sateen fabric she purchased?
Write a system of equations where x is the number of yards of regular quilting fabric purchased and y
is the number of yards of sateen fabric purchased.
Equation 1: Amount of fabric
Equation 2: Cost of fabric
The correct answer is:_________
Example 2 Baseball Game Two families go to a baseball game. One family purchases two adult
tickets and three youth tickets for $33. Another family purchases three adult tickets and two youth
tickets for $37. Let x represent the cost in dollars of one adult ticket and let y represent the cost in
dollars of one youth ticket.
a. Wrtie a linear system to represent this problem:
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b. Solve the linear system to find the cost of one adult and one youth ticket.
c. How much would it cost two adults and five youths to attend the game?
Example 3 Asian Cuisine A group of your friends goes to a restaurant that features different
Asian foods. There are eight people in your group. Some of the group order the Thai special for
$14.25 and the rest of the group order the Szechwan special for $13.95. If the total bill was
$113.10, how many people ordered each dinner?
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Guided Practice:
1. SOCCER A sports equipment store is having a sale on soccer balls. A soccer coach purchases 10
soccer balls and 2 soccer ball bags for $155. Another soccer coach purchases 12 soccer balls and 3
soccer ball bags for $189. Write and solve a system of equations to find the cost of a soccer ball (x)
and the cost of a soccer ball bag (y).
2. Electricians Two different electrical businesses charge different rates.
Business A charges $30 for a service call, plus an additional $45 per hour for labor. Business B
charges $45 for a service call, plus an additional $40 per hour for labor.
a. Let x represent the number of hours of labor and let y represent the total charge in dollars.
Write and solve a linear system that you could use to find the lengths of a service call for
which both businesses charge the same amount.
b. When will the businesses charge the same amount?
3. A business center charges a flat fee to send faxes plus a fee per page. You send one fax with four
pages for $5.36 and another fax with with seven pages for $7.88. What do they charge for the flat
fee? What do they charge per page?
4. Getting to School You walk 1.75 miles to school at an average speed r (in miles per hour). On
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r. The round trip
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took a total of 90 minutes. Find the average speed for each leg of your trip.
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the way back home, you are walking with a friend and your average speed is