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
Then 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.

The brute strength method determines if each x and y value satisfies both conditions. To do this, we must iterate through each result in the specified range and insert them into both models.

What are Elegant mathematical technique?

ALGORITHM :

1. Take the values of all coefficients and SET flag = FALSE

2. Run a FOR loop for x in range (-10, 11). 11 won't be included.

2a. Inside the first FOR, start the y FOR loop in range(-10,11). 11 won't be included

2b. Inside the y FOR loop, check IF for a particular value of x and y both the equations satisfied.

2c. If yes, set flag TRUE and print values of x and y.

2d. ELSE the flag stays FALSE.

END FOR Y

END FOR X

3. Check if flag = FALSE, then print NO SOLUTION

PYTHON CODE :

a=int(input()) #taking input for each coefficient

b=int(input())

c= int(input())

a1= int(input())

b1= int(input())

c1= int(input())

flag = False

for x in range(-10,11): #checking for all values of x in range -10 to 10

for y in range(-10,11): #checking for all values of x in range -10 to 10

if (a x + b y – c == 0) and (a1*x + b1*y - c1 == 0) : #checking if the x and y values satisfy the equation

flag = True #setting the flag if solution is found

print('Solution : x = {-10, 10}, y = {-10, 10}'.format(x,y)) #if they satisfy print x & y

if flag = False : #if flag stays false, that means there is no solution

print('No solution')

OUTPUT : The output is given below.

More about the Elegant mathematical technique link is given below.

https://brainly.com/question/27934739

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