This is a C++ Program that Solves any Linear Equation in One Variable.

Problem Description

The Problem states that given a linear equation in one variable of the form aX + b = cX + d where a,b,c,d are provided as input, we need to determine the appropriate value of X.

Problem Solution

Solving the equation aX + b = cX + d, we get
=> aX – cX = d – b
=> X = (d-b) / (a-c)
So we can solve the equation by applying the above formula. But, we need to figure out following 2 cases of inputs:
Case-1:

    Now if a==c but b!=d, the equation will reduce to:
    X = (d-b)/0
    Hence this value is invalid.

Case-2:

    Now if a==c but b==d, the equation will reduce to:
    aX = cX
    => X = X (Since a=c)
    Hence, any value of X will satisfy the equation and we get infinite number of solutions.

Expected Input and Output

Case-1:

Case-2:

    a=2,b=5,c=2,d=5
    Infinite Solutions

Case-3:

    a=2,b=5,c=2,d=3
    Wrong Equation: No Solution

Program/Source Code

Here is source code of the C++ Program to Solve any Linear Equation in One Variable. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

    #include <bits/stdc++.h>
    using namespace std;
    void solve(float a, float b, float c, float d)
    {
        if(a==c && b==d)
            cout<<"Infinite Solutions"<<endl;
        else if(a==c)
            cout<<"Wrong Equation: No Solution"<<endl;
        else
        {
            float X = (d-b)/(a-c);
            cout<<"Solution is X = "<<X<<endl;
        }
    }
    int main()
    {
        float a, b, c, d;
        cout<<"For a linear equation in one variable of the form aX + b = cX + d"<<endl;
        cout<<"Enter the value of a : ";
        cin>>a;
        cout<<"Enter the value of b : ";
        cin>>b; 
          cout<<"Enter the value of c : ";
        cin>>c; 
        cout<<"Enter the value of d : ";
        cin>>d;
         solve(a, b, c, d);
    }
Program Explanation
main() – In this function, we take the inputs of a,b,c,d and we compute the result inside the function solve().
solve() – Inside this, we check for the cases defined above and we provide appropriate solution.

Runtime Test Cases

Case-1:
$ g++ Variable_Linear_Eq.cpp
$ ./a.out
For a linear equation in one variable of the form aX + b = cX + d
Enter the value of a : 2
Enter the value of b : 4
Enter the value of c : 4
Enter the value of d : 8
Solution is X = -2
Case-2:
$ ./a.out
For a linear equation in one variable of the form aX + b = cX + d
Enter the value of a : 2
Enter the value of b : 5
Enter the value of c : 2
Enter the value of d : 5
Infinite Solutions  
Case-3:
$ ./a.out
For a linear equation in one variable of the form aX + b = cX + d
Enter the value of a : 2
Enter the value of b : 5
Enter the value of c : 2
Enter the value of d : 3
Wrong Equation: No Solution