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

/*********************************************************************************
* (Algebra: 2 * 2 linear equations) Design a class named LinearEquation for a    *
* 2 * 2 system of linear equations:                                              *
*                                                                                *
*  ax + by = e, cx + dy = f; x = (ed - bf) / (ad - bc) y = (af - ec) / (ad - bc) *
*                                                                                *
* 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 - bc is not 0.           *
* ■ Methods getX() and getY() that return the solution for the equation.         *
*                                                                                *
* Draw the UML diagram for the class and 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.                                      *
*********************************************************************************/
import java.util.Scanner;

public class Exercise_09_11 {
	/** Main method */
	public static void main(String[] args) {
		// Create a Scanner object
		Scanner input = new Scanner(System.in);

		
		// Prompt the user to enter a, b, c, d, e, and f
		System.out.print("Enter a, b, c, d, e, f: ");
		double a = input.nextDouble();
		double b = input.nextDouble();
		double c = input.nextDouble();
		double d = input.nextDouble();
		double e = input.nextDouble();
		double f = input.nextDouble();

		// Create a LinearEquation object
		LinearEquation linearEquation = new LinearEquation(a, b, c, d, e, f);
		
		// Display results
		if (linearEquation.isSolvable()) {
			System.out.println("x is " + linearEquation.getX() +
				" and y is " + linearEquation.getY());
		}
		else
			System.out.println("The equation has no solution.");
	}
}

LinearEquation.java

// UML diagram
/*****************************************************
*                    LinearEquation                  *
*----------------------------------------------------*
* -a: double                                         *
* -b: double                                         *
* -c: double                                         *
* -d: double                                         *
* -e: double                                         *
* -f: double                                         *
* +LinearEquation(a: double, b: double, c: double,   * 
*                 d: double, e: double, f: double)   *
* +getA(): double                                    *
* +getB(): double                                    *
* +getC(): double                                    *
* +getD(): double                                    *
* +getE(): double                                    *
* +getF(): double                                    *
* +isSolvable(): boolean                             *
* getX(): double                                     *
* getY(): double                                     *
*****************************************************/

// Implement LinearEquation class
public class LinearEquation {
	// Data fields
	private double a;
	private double b;
	private double c;
	private double d;
	private double e;
	private double f;

	/** Constructor with arguments for a, b, c, d, e, and f */
	LinearEquation(double a, double b, double c, double d, double e, double f) {
		this.a = a;
		this.b = b;
		this.c = c;
		this.d = d;
		this.e = e;
		this.f = f;
	}

	/** Methods */
	/** Return a */
	public double getA() {
		return a;
	}

	/** Return b */
	public double getB() {
		return b;
	}

	/** Return c */
	public double getC() {
		return c;
	}

	/** Return d */
	public double getD() {
		return d;
	}

	/** Return e */
	public double getE() {
		return e;
	}

	/** Return f */
	public double getf() {
		return f;
	}

	/** Returns true if ad - bc is not 0 */
	public boolean isSolvable() {
		return a * d - b * c != 0;
	}

	/** Returns x */
	public double getX() {
		return (e * d - b * f) / (a * d - b * c);
	}

	/** Returns y */
	public double getY() {
		return (a * f - e * c) / (a * d - b * c);
	}
}