(Algebra: solve linear equations) Write a method that solves the following 2 * 2 system of linear equations:

/*********************************************************************************
* (Algebra: solve linear equations) Write a method that solves the following     *
* 2 * 2 system of linear equations:                                              *
* The method header is                                                           *
*                                                                                *
* public static double[] linearEquation(double[][] a, double[] b)                *
*                                                                                *
* The method returns null if a00a11 - a01a10 is 0. Write a test program that     *
* prompts the user to enter a00, a01, a10, a11, b0, and b1, and displays the     *
* result. If a00a11 - a01a10 is 0, report that “The equation has no solution.”   *
* A sample run is similar to Programming Exercise 3.3.                           *
*********************************************************************************/
import java.util.Scanner;

public class Exercise_08_30 {
	/** Main method */
	public static void main(String[] args) {
		// Create a Scanner
		Scanner input = new Scanner(System.in);

		// Create a 2 x 2 matrix
		double[][] a = new double[2][2];

		// Create an array of length 2
		double[] b = new double[2];

		// Prompt the user to enter a00, a01, a10, a11, b0, and b1
		System.out.println("Enter a00, a01, a10, a11, b0, and b1:");
		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				a[i][j] = input.nextDouble();
			}
		}
		for (int i = 0; i < b.length; i++) {
			b[i] = input.nextDouble();
		}

		// Display the result of the linear equation
		double[] result = linearEquation(a, b);
		if (result == null)
			System.out.println("The equation has no solution.");
		else {
			System.out.println("x is " + result[0] + " and y is " + result[1]);
		}
	}

	/** linearEquation solves a 2 x 2 system of linear equations */
	public static double[] linearEquation(double[][] a, double[] b) {
		if (a[0][0] * a[1][1] - a[0][1] * a[1][0] == 0)
			return null;

		double[] r = new double[2]; // Results x and y
		r[0] = (b[0] * a[1][1] - b[1] * a[0][1]) / 
				 (a[0][0] * a[1][1] - a[0][1] * a[1][0]);

		r[1] = (b[1] * a[0][0] - b[0] * a[1][0]) /
				 (a[0][0] * a[1][1] - a[0][1] * a[1][0]);

		return r;
	}
}