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(8) Lesson 3.8
1. Course 3, Lesson 3-8
1. Last year, Justin and his sister, Karin, earned a total of $468 in
allowance. If Justin earned $52 more than Karin in allowance,
write a system of equations that represents their allowances.
2. Mrs. Kung spent the same amount on two programs at the local
recreation center. The aerobics class costs an initial fee of $10
plus $3 per class. The pottery class costs an initial fee of $6 plus
$5 per class. Write a system of equations to represent the cost
for the two programs.
3. The sum of Dewan’s age and three times Adrianne’s age is 32.
The difference between Dewan’s age and Adrianne’s age is 4.
Write a system of equations that can be used to find Dewan’s
age and Adrianne’s age.
2. Course 3, Lesson 3-8
ANSWERS
1. j + k = 468
j = 52 + k
2. 10 + 3x = y
6 + 5x = y
3. d + 3a = 32
d – a = 4
3. WHY are graphs helpful?
Expressions and Equations
Course 3, Lesson 3-8
8. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
1. Solve the system of equations algebraically.
y = x – 3
y = 2x
Since y is equal to 2x, you can replace y with 2x in the first equation.
y = x – 3
Graph the system.Check
Since x = –3 and y = 2x, then y = –6 when x = –3.
The solution of this system of equations is (–3, –6).
7
Write the equation.
2x = x – 3 Replace y with 2x.
Subtraction Property of Equality
x = –3 Simplify.
–x = –x
10. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
2. Solve the system of equations algebraically.
y = 3x + 8
8x + 4y = 12
Since x = –1, replace x with –1 in the equation
y = 3x + 8 to find the value of y.
The solution of this system is (–1, 5).
Write the equation.
8x + 4(3x + 8) = 12 Replace y with 3x + 8.
Collect like terms.20x + 32 = 12
Subtraction Property of Equality
8x + 4y = 12
Distributive Property
8x + 12x + 32 = 12 Simplify.
8x + 4 • 3x + 4 • 8 = 12
Simplify.
Division Property of Equality
Simplify.
20x = –20
x = –1
y = 3(–1) + 8 or 5
y = 3x + 8
–32 = –32
12. 1
Need Another Example?
2
3
Step-by-Step Example
3. A total of 75 cookies and cakes were donated for a bake sale to raise
money for the football team. There were four times as many cookies
donated as cakes.
Write a system of equations to represent this situation.
Draw a bar diagram. Then write the system.
y = 4x There were 4 times as many cookies donated as cakes.
x + y = 75 The total number of cakes and cookies is 75.
13. Answer
Need Another Example?
A store sold 84 black and gray T-shirts one
weekend. They sold 5 times as many black
T-shirts as gray T-shirts. Write a system of
equations to represent this situation.
Sample answer: b + g = 84; b = 5g
14. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
4. A total of 75 cookies and cakes were donated for a bake sale
to raise money for the football team. There were four times as
many cookies donated as cakes. The situation can be
represented by y = 4x and x + y = 75. Solve the system
algebraically. Interpret the solution.
Since y is equal to 4x, you can replace y with 4x.
x = 15 Simplify.
Since x = 15 and y = 4x, then y = 60 when x = 15.
The solution is (15, 60). This means that 15 cakes
and 60 cookies were donated.
x + y = 75 Write the equation.
x + 4x = 75 Replace y with 4x.
5x = 75 Simplify.
Division Property of Equality
15. Answer
Need Another Example?
A store sold 84 black and gray T-shirts one
weekend. They sold 5 times as many black
T-shirts as gray T-shirts. The situation can be
represented by b + g = 84 and b = 5g.
Solve the system algebraically. Interpret the solution.
(70, 14); The store sold 70 black and
14 gray T-shirts.
16. How did what you learned
today help you answer the
WHY are graphs helpful?
Course 3, Lesson 3-8
Expressions and Equations
17. How did what you learned
today help you answer the
WHY are graphs helpful?
Course 3, Lesson 3-8
Expressions and Equations
Sample answer:
• You can use a graph to check the solution to a system
of equations that was solved algebraically.
18. Solve the system of
equations and
x = y – 6
algebraically.
Ratios and Proportional RelationshipsExpressions and Equations
x y
1
15
2
Course 3, Lesson 3-8