Mathematics: Two-by-two linear systems.
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Solving two-by-two linear systems. |
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Two-by-two linear systems are part of most mathematics courses. Such systems are made of 2 linear equations in 2 variables; gerneral form:
a1x + b1y = c1
a2x + b2y = c2
The variables x and y must satisfy both equations. The system may have one unique solution (with x and y being unique real numbers), no solution
or an infinity of solutions.
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If you are not sure how to proceed to solve this kind of equations, you may want to have a look at my math tutorial: 2-by-2 and 3-by-3 linear equation systems.
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Two-by-two linear systems online exercise generator. |
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My online web application is based on my Free Pascal desktop application Equations2. Click the following link to
view the description of the "Equations2" PC application. The application generates a system of
2 equations in their simplest form (just as described above) and the user has to enter the system's solution.
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Use the following link to start the online application. For details about the Perl source code, see below...
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Two-by-two linear systems Perl script. |
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Click the following link to download the Two-by-two linear systems Perl
script and all other files needed to run this application on your web server. Have a look at the ReadMe.txt file, included in the download archive, for details
about the different files, and where to place them on the server.
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The Perl script is rather long and I do not display the source code here. Just some remarks, concerning how the application works:
- The parameter $action tells the script what to do:
- init, new: initialize for a new test (default settings for init, previous test settings for new).
- start, next: generate a new equation (first question for start, all other questions for next).
- check: check user's answer.
- The test web page is generated by reading a template file and replacing all custom
tags (template lines containing a tag start with '#' and all tags are placed between '#' symbols) by the corresponding actual values. What will be displayed
on the page depends on the $action parameter, of course. When all equations are done, an evaluation grid with number of correct and false
answers and success percentage is displayed.
- All code concerning the generation of the equation system is located in the generateSystem subroutine. The function generates 2
random equations ax + by = e and cx + dy = f, eliminating equations where x or y are "missing" in both equations and equations like 0x + 0y = k or 1x + 1y = k.
Before being displayed, the generated equation strings are modified by the subroutine formatEquation, that ensures a proper display
(correcting expressions like "0x", "-1x" or " + 0", for example).
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If you want to place a link to the application on some other page, include the following into this page's HTML:
<a href="/cgi-bin/equations2.pl?action=init">Two-by-two linear systems online application</a>
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