Question

Design a Python class named HomogenEquation for a system of 2x2 linear homogeneous equations:

ax+by=e cx+dy=f

The class should contain:

• The data fields a, b, c, d, e and f.

• A constructor with the arguments a, b, c, d, e and f.

• A method named isSolvable() that returns true if − is not 0.

• The method getXY() that returns the solution for the equation.

Write a test program that prompts the user to enter a, b, c, d, e and f and displays the result. If the equation is not solvable, report that “The equation has no solution.”

Answer 1

The below is the code for the above problem statement:

---------------------------------------------------------------CODE---------------------------------------------------------------------

import numpy as np
class HomogenEquation:
   def __init__(self,a,b,c,d,e,f):
       self.a=a
       self.b=b
       self.c=c
       self.d=d
       self.e=e
       self.f=f
   def isSolvable(self):
       '''
           The linear equation is only solvable
           if (a/b) != (d/e)
           otherwise the equation does not posses an
           unique solution
       '''
       if (self.a/self.b)-(self.d/self.e) != 0:
           return True
       else:
           return False
   def getXY(self):
       '''
           We solve the linear equation with the help of the
           built in function solve() which is defined inside
           numpy.linalg
       '''
       A=np.array([[self.a,self.b],[self.d,self.e]])
       B=np.array([self.c,self.f])
       x,y=np.linalg.solve(A,B)
       return x,y

#Driver Function to Test the functionality of the class
def main():
   a,b,c=map(int,input("Enter Values of a,b,c : ").split())
   d,e,f=map(int,input("Enter Values of d,e,f : ").split())
   Eq=HomogenEquation(a,b,c,d,e,f)
   if Eq.isSolvable():
       x,y=Eq.getXY()
       print("X = ",x,"\nY = ",y)
   else:
       print("The equation has no solution.")
main()

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Code in sublime text:

OUTPUT: