Chapter 11 Additional Topics

SSM: Intermediate Algebra
Section 11.8 Quiz
33.
( )
y = 2 3 − 4
= 6 − 4
= 2
( )
y = 2 2 − 4
= 4 − 4
= 0
The solutions are ( 3,2 ) and ( )
satisfies both equations.
x
2 2
+ y = 25
2 2
4x
− 25y
= 100
2 2
4x
+ 25y
= 100
y
2,0 . Each result
Section 11.8 Quiz
1. x
2 y
2
9 + = 81
x
2 2
+ y = 9
y
8
(−3,0) (3,0)
−8
8
−8
x
4
(−5,0) (5,0)
−4
The two intersection points for all three graphs
5,0 5,0 . These are the solutions to
are ( − ) and ( )
the system. Each result satisfies all three
equations.
35. Answers may vary. One possible answer:
2 2
x + y = 16
x
2 2
− y = 16
37. 2x
2 + cy
2 = 82
2
y = x + dx + 5
Substitute ( 1,4 ) into each equation.
( ) c( )
2 2
2 1 + 4 = 82
2 + 16c
= 82
16c
= 80
c = 5
x
2
( ) d ( )
4 = 1 + 1 + 5
4 = 1+ d + 5
d = −2
39. Written response. Answers may vary.
2.
The two intersection points ( − 3,0)
and ( 3,0 )
are the solutions to the system.
Solve using elimination.
2 2
9x
+ y = 81
2 2
−9x
− 9y
= −81
2
− 8y
= 0
y
2
= 0
y = 0
Let y = 0 in
x
x
2 2
+ y = 9
2 2
+ 0 = 9
x
2
= 9
x = ± 3
x
2 2
+ y = 9 and solve for x.
The solutions are ( − 3,0)
and ( )
2
y = x − 2
y = − 2x
+ 1
(−3,7)
y
8
3,0 .
−4
−2 2 4
(1, −1)
x
The two intersection points ( 1, − 1)
and ( − 3,7)
are the solutions of the system.
Solve using substitution.
2
Substitute x − 2 for y in the second equation.
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