Download Math 40 Chapter 7 Lecture Notes

Math 40
Chapter 7
Lecture Notes
Professor Miguel Ornelas
1
M. Ornelas
Math 40 Lecture Notes
Section 7.1
Section 7.1
Systems of Equations and Graphing
Three Cases
y
y
y
x
x
x
Solving a System by Graphing
Solve each system by graphing:
y
5
x+y =7
4
y = 3x − 1
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5
1
2
3
4
5
x
-1
-2
-3
-4
-5
y
5
2x + y = 8
4
x−y =7
3
2
1
-5
-4
-3
-2
-1
-1
-2
-3
-4
-5
Section 7.1 continued on next page. . .
2
x
M. Ornelas
Math 40 Lecture Notes
Section 7.1 (continued)
y
5
x + 2y = 7
4
3x + 6y = 21
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5
1
2
3
4
5
x
-1
-2
-3
-4
-5
y
5
4x − 20 = 5y
4
8x − 10y = 20
3
2
1
-5
-4
-3
-2
-1
-1
-2
-3
-4
-5
Section 7.2
System of Equations and Elimination
Use the elimination method to solve each system.
x − 5y = −12
−x + y =
x+ y = 6
−x + 2y = 15
4
Section 7.2 continued on next page. . .
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x
M. Ornelas
Math 40 Lecture Notes
Section 7.2 (continued)
4x − 10y = 13
4x − 3y = 2
−2x + 5y = 8
8x − 6y = 4
Section 7.3
Systems of Equations and Substitution
Use the substitution method to solve each system.
3x − y = − 8
3x + 2y = 2
x=y−6
y = 6x + 3
3x − 6y = 2
x − 2y = 7
3x − 21 = 6y
x = 2y + 1
Section 7.3 continued on next page. . .
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M. Ornelas
Math 40 Lecture Notes
Section 7.3 (continued)
Section 7.4
Applications Using Systems
Basketball Scoring
In a recent game, Kevin Durant of the Oklahoma City Thunder scored 24 points on a combination of 11
two-point and three-point baskets. How many shots of each type were made?
Define Variables
System of Equations
Solve System
Sentence
Finding the Number of Tickets
If tickets for a show cost $2.00 for adults and $1.50 for children, how many of each kind of ticket were sold
if a total of 300 tickets were sold for $525?
Define Variables
System of Equations
Solve System
Sentence
Section 7.4 continued on next page. . .
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M. Ornelas
Math 40 Lecture Notes
Section 7.4 (continued)
Finding the Number of Coins
If Thomas has 15 coins totaling $2.70, and the coins are quarters and dimes, how many of each coin does he
have?
Define Variables
System of Equations
Solve System
Sentence
Finding the Amount Invested
Conrad invests $17,000 in two accounts. One account earns 5% interest per year and the other earns 6.5%.
If his total interest after one year is $970, how much did he invest at each rate?
Define Variables
System of Equations
Solve System
Sentence
Section 7.4 continued on next page. . .
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M. Ornelas
Math 40 Lecture Notes
Section 7.4 (continued)
Mixing Solutions
Brand X window cleaner is 12% alcohol and Brand Y window cleaner is 30% alcohol. How much of each
cleaner should be used to make 90 oz of a cleaner that is 20% alcohol?
Define Variables
System of Equations
Solve System
Sentence
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