Transcript Algebra 2

Solve by Using Substitution
Use substitution to solve the system of equations.
x + 4y = 26
x – 5y = –10
Solve the first equation for x in terms of y.
x + 4y = 26
x = 26 – 4y
First equation
Subtract 4y from each side.
Solve by Using Substitution
Substitute 26 – 4y for x in the second equation and
solve for y.
x – 5y = –10
26 – 4y – 5y = –10
–9y = –36
y=4
Second equation
Substitute 26 – 4y for x.
Subtract 26 from each side.
Divide each side by –9.
Solve by Using Substitution
Now substitute the value for y in either of the original
equations and solve for x.
x + 4y = 26
x + 4(4) = 26
x + 16 = 26
x = 10
First equation
Replace y with 4.
Simplify.
Subtract 16 from each side.
Answer: The solution of the system is (10, 4).
Solve the system of equations using substitution.
What is the solution to the system of equations?
x – 3y = 2
x + 7y = 12
D. (5, 1)
C.
C
D.
D
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D
B
C
C. (8, 2)
B.
B
B.
A. A
A
A. (1, 5)
Solve by Substitution
Lancaster Woodworkers Furniture Store builds two
types of wooden outdoor chairs. A rocking chair
sells for $265 and an Adirondack chair with
footstool sells for $320. The books show that last
month, the business earned $13,930 for the 48
outdoor chairs sold. How many of each chair were
sold?
Read the Test Item
You are asked to find the number of each type of
chair sold.
Solve by Substitution
Solve the Test Item
Step 1 Define variables and write the system of
equations. Let x represent the number of
rocking chairs sold and y represent the number
of Adirondack chairs sold.
x + y = 48
265x + 320y = 13,930
The total number of chairs
sold was 48.
The total amount earned
was $13,930.
Solve by Substitution
Step 2 Solve one of the equations for one of the
variables in terms of the other. Since the
coefficient of x is 1, solve the first equation for
x in terms of y.
x + y = 48
x = 48 – y
First equation
Subtract y from each side.
Solve by Substitution
Step 3 Substitute 48 – y for x in the second equation.
265x + 320y = 13,930
265(48 – y) + 320y = 13,930
12,720 – 265y + 320y = 13,930
55y = 1210
y = 22
Second equation
Substitute 48 – y for x.
Distributive Property
Simplify.
Divide each side by 55.
Solve by Substitution
Step 4 Now find the value of x. Substitute the value
for y into either equation.
x + y = 48
x + 22 = 48
x = 26
First equation
Replace y with 22.
Subtract 22 from each side.
Answer: They sold 26 rocking chairs and 22
Adirondack chairs.
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AMUSEMENT PARKS At Amy’s Amusement Park,
tickets sell for $24.50 for adults and $16.50 for
children. On Sunday, the amusement park made
$6405 from selling 330 tickets. How many of each
kind of ticket was sold?
A. A
A. 210 adult; 120 children
B. B
B. 120 adult; 210 children
C. C
C. 300 children; 30 adult
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D. D
D. 300 children; 30 adult