02-09_task
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University of Texas *
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Course
QUADRATICS
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
2
Uploaded by MegaThunderBadger24
Name:
Evan Swain
Date:
10/1/22
School:
Columbia HS
Facilitator:
2.09 Linear Systems (40 Points)
Solve each system of equations.
1.
Solve the system.
5
x
+ 5
y
– 4
z
= 13
5
x
+ 3
y
+
z
= –3
3
x
– 2
y
–
z
= –10
Answer:
x
=
-2
,
y
=
3
,
z
=
-2
2.
Solve the system.
x
– 4
y
–
z
= 21
6
x
– 3
y
–
z
= –4
–
x
+2
y
–5
z
= 19
Answer:
x
=
-4
,
y
=
-5
,
z
=
-5
Solve each system using any method from this Unit.
3.
A concert is being held in your hometown. 1500 tickets are sold. Adult tickets are $10.50
and child’s tickets are $7.50. If a total of $13950 worth of tickets were sold, determine
how many adult tickets and how many child tickets were sold.
Answer: Let
x
be the number of adult tickets and
y
be the number of child tickets. System of
equations:
1
st
equation:
x+y=1500
2
nd
equation:
10.50x+7.50y=19350
Solution:
x
=
900
and
y
=
600
4.
Johnny invested $20,000. A portion returned 5% and another portion returned 8%. The
total interest earned on the investment was $1150. Write a system of equations for this
© ACCESS Virtual Learning 2021
situation and determine how much of the original investment was invested at the 5% rate
and how much was invested at the 8% rate.
Answer: Let
x
be the amount invested that earned 5% and
y
be the amount invested that
earned 8%. System of equations:
1
st
equation:
x+y=20000
2
nd
equation:
Solution:
x
= $
15000
,
y
= $
5000
.
Solve the system by writing a matrix equation, then solve using the inverse with a
calculator. Make sure and enter your matrix equation in space provided below
5.
You have 37 coins that are nickels, dimes, and pennies. The total value of the coins is
$1.55. There are twice as many pennies as dimes. Find the number of each type of coin in
the bank.
Answer: Let
n
be the number of nickels,
d
be the number of dimes, and
p
be the number of
pennies. The system is
1
st
equation:
p=2d
2
nd
equation:
p-2d=0
3
rd
equation:
p+0n-2d
Matrix Equation:
The solution is
20
pennies,
10
dimes and
7
nickels.
© ACCESS Virtual Learning 2021
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