Unit 6 Day 1: Standard 8.1 (day 1)
Standard:
Use and solve systems of linear equations with
two variables algebraically. Be able to solve systems
of linear equations given a contextual situation.
Novice:
Find the solution to a linear system given a
graph or a point.
Developing:
Find the solution to a linear system
algebraically
Proficient:
Be able to solve systems of linear equations
given a contextual situation.
1
Warm Up
#1. Tell whether (-3, 5) is a solution of the system:
2x + 4y = 14
3x + 2y = 10
#2. Find the solution to the system by graphing.
Then be sure to check your answer algebraically.
2x - 3y = -3
4x + y = 1
#3. Solve the system algebraically.
3x - 2y = 13
x - 3y = 2
#4. Solve the system algebraically.
2x + 5y = 3
3x + 10y = -2
2
Warm Up
#1. Tell whether (-3, 5) is a solution of the system:
2x + 4y = 14
3x + 2y = 10
3
Warm Up
#2. Find the solution to the system by graphing.
Then be sure to check your answer algebraically.
2x - 3y = -3
4x + y = 1
4
Warm Up
#3. Solve the system algebraically.
3x - 2y = 13
x - 3y = 2
5
Warm Up
#4. Solve the system algebraically.
2x + 5y = 3
3x + 10y = -2
6
Solving Systems Given
Contextual Situations
7
How do you know when
substitution or elimination is
"better" and more efficient to use
when trying to solve a system of
linear equations?
8
Solving Contextual Situations
9
Solving Contextual Situations
Office Depot sells two types of fax machines. They charge $150
for one of the machines and $225 for the other. If the company
sold 22 fax machines for a total of $3900 last month, how many
of each type of fax machine was sold?
10
Solving Contextual Situations
The St. Louis Art Museum collected $1590 from 321 people
yesterday. Adult admission to the museum is $6 and child
admission is $4. How many adults and how many children
visited the museum yesterday?
11
Solving Contextual Situations
My grandmother sews both large and small quilts. A large quilt
requires 8 yards of fabric, while the small quilt requires 3 yards of
fabric. How many of each size quilt was made if she used a total
of 90 yards of fabric to make 15 quilts?
12
Solving Contextual Situations
For extremely cold temperatures, a car manufacturer recommends
that a 70% antifreeze and 30% water mix be used in the cooling
system of a car. How many quarts of pure (100%) antifreeze and
a 50% antifreeze and 50% water mix should be combined to
make 11 quarts of a 70% antifreeze and 30% water mixture?
13
Solving Contextual Situations
Mr. Jauss, a South High chemistry teacher, needs 15 liters of a
60% alcohol solution. He has a solution that is 50% alcohol. How
many liters of the 50% alcohol solution and pure alcohol should he
mix together to make 15 liters of a 60% alcohol solution?
14
Solving Contextual Situations
The St. Louis Mississippi Riverboat Cruise travels 28 miles
upstream in 7 hours. It travels 28 miles downstream in 5
hours. The speed of the current remains the same during the
entire trip. Find the average speed of the riverboat in still
water and the speed of the current.
15
Solving Contextual Situations
Your brother is in France for a semester and has a choice of two
Internet cafes. Cafe de Flore charges $12 plus $2 an hour. Cafe Le
Paris charges $27 plus $0.50 an hour.
a) How many hours would he need to use the Internet per month for
the services to be the same price?
b) He estimates that he will spend between 15 and 20 hours per
month on the Internet. Which cafe should he choose?
16
Solving Contextual Situations
17
Solving Contextual Situations
18
Solving Contextual Situations
19
Classwork:
Standard 8.1 Classwork (day 2)
Homework:
Worksheet 8.1B
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