Expert: Abe Mantell - 7/15/2008

Question
QUESTION: How can i write a system of equation with a unique solution, an infinite number of solutions, and with no solution.

ANSWER: Hello Elisa,

How many unknowns would you like?

Let's consider 2-variables.

1. Unique solution ==> non-parallel lines ==> Lines with different slopes
-- For example: x+y=1 & x+2y=1

2. Infinite # of solutions ==> Lines are the same, so they intersect
-- everywhere ==> For example: x+y=1 & 2x+2y=2

3. No solution ==> Lines are parallel but not the same lines
-- For example: x+y=1 & x+y=2

OK?

Abe


---------- FOLLOW-UP ----------

QUESTION: 1. A new virus is released on the internet; the administrator of a department's Local Area Network ( LAN) is given five minutes by a manager to estimate the impact. The administrator samples 15 of the PCs connected to the LAN, and finds that 9 are infected; use proportion to estimate the number of infected PCs if there are a total of 202 PCs connected to the LAN.

2. An administrator of a popular web site is told that a new server can handle 41,000 "hits" (users accessing the site) per second. The web site currently experiences a peak demand of about 105,000 hits per second; but every month, the peak demand increases by 2800 hits per second. Use a proportion equation to determine how many new servers the administrator should buy to address expected traffic for the next 24 months.


Answer
Hello again Elisa,

1. 9/15 = x/202, where x=the number infected out of the 202.
-- solving for x: x=(9/15)*202=121.2, rounded to 121.

2. Assuming the servers are all purchased now, rather than over the
-- 24 month period ==> 2800 x 24 = 67200 more hits in 24 months.
-- so they will need to cover 105000 + 67200 hits = 172200 hits.
-- Let x=the number of servers needed ==> 41000x = 172200
-- x=172200/4100=42 servers.

Abe