Solving Linear Equations in One Variable Using C

This is a C Program to solve any linear equation in one variable.

Problem Description

For linear equation of the form aY + b + c = 0, we need to input value of a,b,c. After having values of all the constants we need to solve for Y and create a function which will return the calculated value of Y.

Expected Input and Output

Case 1. When the coefficient of Y is zero.

If a = 0, then we cannot predict the value of Y
because the product "a*Y" in the equation will become 0.

Case 2. When all the constants are positive:
For example:

If the value of a = 1, b = 1 and c = 1
then Y = -2.

Case 3. When constants are both negative and positive:
For example:

If the value of a = 1, b = -2 and c = -1
then Y = 3.

Problem Solution

1. Input the values of a,b,c.
2. Put them in the given equation and make the resulting equation equal to 0.
3. Solve for Y.

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Program/Source Code

Here is source code of solving any linear equation in one variable. The program is successfully compiled and tested using Codeblocks gnu/gcc compiler on windows 10. The program output is also shown below.

```
#include <stdio.h>
```
```
#include <string.h>
```

float solve_for_y(float a, float b, float c)

```
{
```
```
     float Y;
```
```
     if(a == 0)
```
```
     {
```

          printf("Value of Y cannot be predicted\n");

```
     }
```
```
     else
```
```
     {
```
```
          Y = -(b + c) / a;
```
```
     }
```
```
    return Y;
```
```
}
```
```
int main()
```
```
{
```
```
  float a, b, c, Y;
```

  printf("\nEnter a linear equation in one variable of the form aY + b + c = 0 ");

  printf("\nEnter the value of a, b, c respectively: ");

```
  scanf("%f%f%f", &a, &b, &c);
```
```
  Y = solve_for_y(a, b, c);
```
```
  printf("\nSolution is Y = %f", Y);
```
```
  return 0;
```
```
}
```

Program Explanation

1. Here in this program we have taken 3 variables a, b and c where a is the coefficient of Y.
2. We have to solve for Y. It can simply evaluated as -(b+c)/a.
3. Since value of Y can have fractional values that is why we have taken its data type as float.

Runtime Test Cases

1. Enter a linear equation in one variable of the form aY + b + c = 0
   Enter the value of a, b, c respectively: 0 1 1
   Value of Y cannot be predicted.
2. Enter a linear equation in one variable of the form aY + b + c = 0
   Enter the value of a, b, c respectively: 1 1 1
 
   Solution is Y = -2.000000
3. Enter a linear equation in one variable of the form aY + b + c = 0
   Enter the value of a, b, c respectively: 1 -2 -1
 
   Solution is Y = 3.000000

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