Question 1.11: Solving a System of Equations with EES The difference of two...

Relations are given for the difference and the sum of the squares of two numbers. They are to be determined.
Analysis We start the EES program by double-clicking on its icon, open a new file, and type the following on the blank screen that appears:

\begin{gathered} x-y=4 \\ x^{\wedge} 2+y^{\wedge} 2=x+y+20 \end{gathered}

which is an exact mathematical expression of the problem statement with x and y denoting the unknown numbers. The solution to this system of two nonlinear equations with two unknowns is obtained by a single click on the “calculator” icon on the taskbar. It gives

x = 5 \quad \text { and } \quad y = 1

Discussion Note that all we did is formulate the problem as we would on paper; EES took care of all the mathematical details of solution. Also note that equations can be linear or nonlinear, and they can be entered in any order with unknowns on either side. Friendly equation solvers such as EES allow the user to concentrate on the physics of the problem without worrying about the mathematical complexities associated with the solution of the resulting system of equations.