Chapter 7 - Solving Multiple Equations; Rational Equation Systems; Example 1 - Projectile Motion - HP 48gII User Manual

Graphing calculator.

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.
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