Chapter 8, Problem 8.30PE

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

$\begin{array}{ccc}\begin{array}{c}{a}_{00}x+a_{01}y=b_0\\ a_{10}x+a_{11}y=b_1\end{array}& x=\frac{b_0{a}_{11}-b_1{a}_{01}}{a_{00}{a}_{11}-a_{01}{a}_{10}}& y=\frac{b_1{a}_{00}-b_0{a}_{10}}{a_{00}{a}_{11}-a_{01}{a}_{10}}\end{array}$

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.