The Use of Mathematica to Solve Simultaneous Equations

In Chapter 3, we introduced the use of Mathematica to solve a single algebraic equation, using the Solve statement and the NSolve statement. The Solve statement can also be used to solve simultaneous equations. The equations are typed inside curly brackets with commas between them, and the variables are listed inside curly brackets. To solve the equations ax + by = c gx +hy = k we type the input entry 

Solve[ a x + by==c, gx + hy== k, x,y ] and press the Enter key. Notice the use of braces to notify Mathematica that we have a list of two equations and a list of two variables and the use of a space to indicate multiplication. The output is 

To simplify the expressions for x and y, we use the fact that the percent S5mibol represents the last line of output and type Simplify[%] 

Donald J. Royer, Bonding Theory, pp. 154-163, McGraw-Hill, New York, 1968. 

The Eliminate statement is used to eliminate one or more of the variables in a set of simultaneous equations. For example, to obtain a single equation in x from the set of equations above, you would type the input entry (note the double equal signs)  

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Students require knowledge of solving (numerically) simultaneous first-order differential equations (initial value problems) and multiple nonlinear algebraie equations. The use of mathematical software that provides numerieal solutions to those types of equations (e.g., Matlab, Mathematica, Maple, Matbead, Polymatb, HiQ, etc.) is required. Numerical solutions of all the examples in the text are posted on the book web page. 

MATHEMATICA is used to solve the partial differential simultaneous equations of the mathematically and thermodynamically coupled systems given in Eqs. (9.69) and (9.70). 

Mathematica can carry out both symbolic and numerical solutions of equations, including single algebraic equations, simultaneous algebraic equations, and differential equations, which we discuss later. Mathematica contains the rules needed for the symbolic solution of polynomial equations up to the fourth degree, and can solve some fifth-degree equations. The principal statements used to solve equations are Solve, FindRoot, Eliminate, and Reduce. 

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