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

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.

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.

Case-1:

a=2,b=4,c=8,d=16 X=-2

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

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);

`}`

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.

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

**Sanfoundry Global Education & Learning Series – 1000 C++ Programs.**