C program to find the solution of linear equation

We can apply the software development method to solve the linear equation of one variable in C programming language. A linear equation of the form ax + b = 0 can be solved by rearranging to find x = -b/a (provided a ? 0).

Syntax

float solve(float a, float b);
x = -b / a;  // where a != 0

Requirements

• The equation should be in the form of ax + b = 0
• a and b are inputs, we need to find the value of x
• Handle the case where a = 0 (no unique solution)

Analysis

Here −

• Input: Coefficients a and b of the linear equation
• Output: The value of x that satisfies the equation
• Special case: When a = 0, the equation becomes b = 0, which has no unique solution for x

Algorithm

Refer to the algorithm given below to find solution of linear equation −

Step 1: Start
Step 2: Read a, b values
Step 3: Check if a == 0
        If true: Print "No unique solution"
        Else: Calculate x = -b/a
Step 4: Print the result
Step 5: Stop

Example

Following is the C program to find the solution of linear equation −

#include <stdio.h>

float solve(float a, float b) {
    float x;
    if (a == 0) {
        printf("No unique solution exists (a cannot be zero)
");
        return 0;
    } else {
        x = -b / a;
        return x;
    }
}

int main() {
    float a, b, x;
    
    printf("Enter coefficients a and b: ");
    scanf("%f %f", &a, &b);
    
    x = solve(a, b);
    
    if (a != 0) {
        printf("For the equation %.2fx + %.2f = 0
", a, b);
        printf("The solution is: x = %.2f
", x);
    }
    
    return 0;
}

Output

When the above program is executed, it produces the following result −

Enter coefficients a and b: 4 8
For the equation 4.00x + 8.00 = 0
The solution is: x = -2.00

Example with Zero Coefficient

Let's see what happens when a = 0 −

#include <stdio.h>

int main() {
    float a = 0, b = 5;
    
    printf("For the equation %.2fx + %.2f = 0
", a, b);
    
    if (a == 0) {
        if (b == 0) {
            printf("Infinite solutions exist (0 = 0)
");
        } else {
            printf("No solution exists (%.2f ? 0)
", b);
        }
    } else {
        float x = -b / a;
        printf("The solution is: x = %.2f
", x);
    }
    
    return 0;
}

For the equation 0.00x + 5.00 = 0
No solution exists (5.00 ? 0)

Key Points

• Always check if the coefficient a is zero to avoid division by zero
• When a = 0 and b ? 0, no solution exists
• When a = 0 and b = 0, infinite solutions exist
• The formula x = -b/a works only when a ? 0

Conclusion

Solving linear equations in C involves basic arithmetic and conditional logic. The key is handling the special case where the coefficient of x is zero, which leads to either no solution or infinite solutions.