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Page 7-1
Chapter 7
Solving multiple equations
Many problems of science and engineering require the simultaneous solutions
of more than one equation. The calculator provides several procedures for
solving multiple equations as presented below. Please notice that no discussion
of solving systems of linear equations is presented in this chapter. Linear
systems solutions will be discussed in detail in subsequent chapters on matrices
and linear algebra.
Rational equation systems
Equations that can be re-written as polynomials or rational algebraic
expressions can be solved directly by the calculator by using the function
SOLVE. You need to provide the list of equations as elements of a vector. The
list of variables to solve for must also be provided as a vector. Make sure that
the CAS is set to mode Exact before attempting a solution using this procedure.
Also, the more complicated the expressions, the longer the CAS takes in solving
a particular system of equations. Examples of this application follow:
Example 1 – Projectile motion
Use function SOLVE with the following vector arguments, the first being the list of
equations: [‘x = x0 + v0*COS(θ0)*t’ ‘y =y0+v0*SIN(θ0)*t – g*t^2/2’]`,
and the second being the variables to solve for, say t and y0, i.e., [‘t’ ‘y0’].
The solution in this case will be provided using the RPN mode. The only reason
being that we can build the solution step by step. The solution in the ALG
mode is very similar. First, we store the first vector (equations) into variable A2,
and the vector of variables into variable A1. The following screen shows the
RPN stack before saving the variables.
At this point, we need only press K twice to store these variables.
To solve, first change CAS mode to
Exact, then, list the contents of A2 and A1,
in that order: @@@A2@@@ @@@A1@@@ .