Homework Assignment #1
Math 67
UC Davis, Fall 2011
Homework due.
Tuesday 10/4/11
at discussion section.
Reading material.
Read Chapters 1–2 and Appendix A in the textbook.
Problems
1. For each of the following systems of linear equations, if the system has a unique
solution, find it; otherwise, indicate if there are no solutions or an infinite number of
solutions.
(a)
x
+
y
=
22
x

2
y
=
7
(b)

4
x
+
2
y
=
10
2
x

y
=
10
(c)
x
+
y
=
10
5
x
+
5
y
=
50
(d)
x
+
2
y
+
3
z
=
11
2
x
+
6
z
=
14
x
+
y
+
z
=
5
2. In the story believed to be the origin of the expression “
Eureka!
”, the Greek mathe
matician Archimedes discovered how to measure the volume of an object by immersing
it in liquid, thereby helping King Hiero II of Syracuse to find out if his goldsmith had
cheated him by using a higher percentage of silver and a smaller one of gold than he
was supposed to in a crown he had been commissioned to make.
Assume that the crown was made of a mixture of gold and silver, weighed 1 pound
(equal to about 454 grams) and had a volume of 30 cubic centimeters. The density of
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