Chapter 9, Problem 9.11PE

(Algebra: 2 × 2linear equations) Design a class named LinearEquation for a 2 × 2 system of linear equations:

$\begin{array}{ccc}\begin{array}{c}ax+by=e\\ cx+dy=f\end{array}& x=\frac{ed-bf}{ad-bc}& y=\frac{af-ec}{ad-bc}\end{array}$

The class contains:

• Private data fields a , b, c, d, e , and f .
• A constructor with the arguments for a, b, c, d, e , and f .
• Six getter methods for a , b, c, d, e, and f .
• A method named isSolvable () that returns true if ad - be is not 0.
• Methods getX () and getY () that return the solution for the equation.

Draw the UML diagram for the class then implement the class. Write a test program that prompts the user to enter a , b, c, d, e , and f and displays the result. If ad − bc is 0, report that “The equation has no solution.” See Programming Exercise 3.3 for sample runs.