We use cookies to give you the best experience possible. By continuing we’ll assume you’re on board with our cookie policy

# Cramer’s Rule

The whole doc is available only for registered users
• Pages: 2
• Word count: 359
• Category: Algebra

A limited time offer! Get a custom sample essay written according to your requirements urgent 3h delivery guaranteed

Order Now

Cramer’s rule is a method for solving linear simultaneous equations. It makes use of determinants and so a knowledge of these is necessary before proceeding.

1. Cramer’s Rule – two equations
If we are given a pair of simultaneous equations a1 x + b1 y = d1 a2 x + b2 y = d2 then x, and y can be found from d1 b1 d2 b2 a1 b1 a2 b2 a1 d1 a2 d2 a1 b 1 a2 b 2

x=

y=

Example Solve the equations 3x + 4y = −14 −2x − 3y = 11

Solution Using Cramer’s rule we can write the solution as the ratio of two determinants. −14 4 11 −3 3 4 −2 −3 −2 = 2, −1 3 −14 −2 11 3 4 −2 −3

x=

=

y=

=

5 = −5 −1

The solution of the simultaneous equations is then x = 2, y = −5.

5.2.1

copyright c Pearson Education Limited, 2000

2. Cramer’s rule – three equations
For the case of three equations in three unknowns: If a1 x + b1 y + c1 z = d1 a2 x + b2 y + c2 z = d2 a3 x + b3 y + c3 z = d3

then x, y and z can be found from d1 d2 d3 a1 a2 a3 b1 b2 b3 b1 b2 b3 c1 c2 c3 c1 c2 c3 a1 a2 a3 a1 a2 a3 d1 d2 d3 b1 b2 b3 c1 c2 c3 c1 c2 c3 a1 a2 a3 a1 a2 a3 b1 b2 b3 b1 b2 b3 d1 d2 d3 c1 c2 c3

x=

y=

z=

Exercises Use Cramer’s rule to solve the following sets of simultaneous equations. a)

7x + 3y = 15 −2x + 5y = −16

b)

x + 2y + 3z = 17 3x + 2y + z = 11 x − 5y + z = −5

Answers a) x = 3, y = −2.

b) x = 1, y = 2, z = 4

##### Related Topics

We can write a custom essay

According to Your Specific Requirements

Order an essay
300+
Materials Daily
100,000+ Subjects
2000+ Topics
Free Plagiarism
Checker
All Materials
are Cataloged Well

Sorry, but copying text is forbidden on this website. If you need this or any other sample, we can send it to you via email.

By clicking "SEND", you agree to our terms of service and privacy policy. We'll occasionally send you account related and promo emails.
Sorry, but only registered users have full access

How about getting this access
immediately?

Your Answer Is Very Helpful For Us
Thank You A Lot!

Emma Taylor

online

Hi there!
Would you like to get such a paper?
How about getting a customized one?

Can't find What you were Looking for?

Get access to our huge, continuously updated knowledge base

The next update will be in:
14 : 59 : 59