Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Linear Systems


Date: 10/22/96 at 20:51:13
From: Brett Farley
Subject: Linear systems
 
I need to solve this system of equations for x and y in terms of a, b, 
c, d, e, and f:

ax + by = e
cx + dy = f

I've come up with:  (x,y) = de - bf    ce - af
                            _______  , _______
                            da - bc    ab - ad 


Date: 10/23/96 at 13:22:35
From: Doctor Ken
Subject: Re: Linear systems

Hi Brett-

Your answer isn't quite right, but it's close.

The correct answer should have been

          / d e - b f    f a - c e \
 (x, y) = | ---------,   --------- |
          \ d a - b c    d a - b c /

x was right, and the numerator for y was right.  So you should try to 
figure out where y got messed up in your equations, and then you'll be 
all set.  

If you go on and study more math, you'll learn some methods that make 
this problem much easier.  Those methods, studied in a class called 
"Linear Algebra," have to do with matrices, which are just tables of 
numbers.  If you're interested in knowing about these, read on!

A matrix is just a bunch of rows and colums.  In your case, we could 
write the problem as

/ a  b \/ x \    / e \
|      ||   |  = |   |
\ c  d /\ y /    \ f /

That's a 2 by 2 matrix times a 2 by 1 matrix, and on the right is a 2 
by 1 matrix.  

Anyway, solving that problem for x and y isn't bad if you know the 
techniques.  But if you don't use matrices and just try to use regular 
high-school algebra techniques, you're likely to take longer and make 
more mistakes. 

-Doctor Ken,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Basic Algebra
High School Linear Algebra

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/