Two points on line 1 are given as (x1, y1) and (x2, y2) and on line 2 as (x3, y3) and (x4,...

Two points on line 1 are given as (x1, y1) and (x2, y2) and on line 2 as (x3, y3) and (x4, y4), as shown in Figure. The intersecting point of the two lines can be found by solving the following linear equation:

(y1 – y2)x – (x1 – x2)y = (y1 – y2)x1 – (x1 – x2)y1

(y3 – y4)x – (x3 – x4)y = (y3 – y4)x3 – (x3 – x4)y3

This linear equation can be solved using Cramer’s rule (see Exercise). If the equation has no solutions, the two lines are parallel (Figure).

Can the following conversions involving casting be allowed? Write a test program to verify your answer.

A linear equation can be solved using Cramer’s rule given in Exercise. Write a 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.”

You can use Cramer’s rule to solve the following 2 × 2 system of linear equation:

Write a program that solves the following equation and displays the value for x and y:

                        3.4x + 50.2y = 44.5

                        2.1x + .55y = 5.9

Write a program that prompts the user to enter four points and displays the intersecting point. Here are sample runs: