Question

4.19 LAB: Brute force equation solver

Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10.

Ex: If the input is:

8 7 38
3 -5 -1
the output is:

x = 3, y = 2
Use this brute force approach:

For every value of x from -10 to 10
For every value of y from -10 to 10
Check if the current x and y satisfy both equations. If so, output the solution, and finish.
Ex: If no solution is found, output:

There is no solution
Assume the two input equations have no more than one solution.

Note: Elegant mathematical techniques exist to solve such linear equations. However, for other kinds of equations or situations, brute force can be handy.
In C programming language NOT C++

Answer 1

Using a brute force approach, all pairs of integers within the specified range are tested until a solution for the set of linear equations is found or it is determined that no solution exists within that range.

Step-by-step explanation:

The task described in the question involves using a brute force approach to finding an integer solution for a set of two linear equations with integer coefficients. In this brute force method, one evaluates all integer pairs (x, y) within a specified range such as -10 to 10, to determine which pair satisfies both equations. If a solution exists within the range, it will be found; otherwise, we conclude that no solution exists within that range. The essential steps include: iterating through all combinations of x and y, substituting these into the given equations, and checking for equality with the respective equation constants.