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# Table of Non-Linear Simultaneous Equations

Journal: International Journal of Science and Research (IJSR) (Vol.10, No. 11)

Publication Date:

Authors : ;

Page : 276-285

Keywords : Non-linear equations; simultaneous equations; Cramer's rule;

### Abstract

Solving non-linear simultaneous equations is not so straightforward as its linear counterpart and is usually a challenge especially for the mathematically average person. The existing methods involve the use of substitution, or in some cases, elimination. This paper introduces a new method of solving various forms of non-linear simultaneous equations via Cramer?s Rule whereby the task is reduced to simple calculations thatrequires nothing more than basic mathematics of addition, subtraction, multiplication, division, square and squareroot of some real numbers, hence making it possible for a person who doesn?t know the substitution procedure at all to be able to determine the correct answers to the said equations. A total of 65 different general forms of non-linear simultaneous equations together with their solutions in closed forms are tabulated in the proposed Table of Non-linear Simultaneous Equations. Hence, for a given set of non-linear simultaneous equations in two variables that matches one of the tabulated forms, one just read off the solutions from the table, plug-in the corresponding constants and perform some simple calculations to obtain the answers. Furthermore, since the computation involve nothing more than straightforward arithmetic, it can be easily programed using basic formula in Excel spreadsheet. One just need to enter the few constants from the two equations into the spreadsheet, the answers will be obtained in a second.