Solving a 2x2 System of Linear Equations

How to Create Custom Functions for Solving Math Problems in Your Calculator

Hello, calculator enthusiasts! Today, I’m going to walk you through how you can create a custom function in your calculator to solve specific math problems. If you're dealing with 2x2 systems of linear equations, this guide is for you. We'll use the provided code as an example and break it down step by step.

The Problem: Solving a 2x2 System of Linear Equations

A 2x2 system of linear equations looks like this:

a * x + b * y = m

c * x + d * y = n

Here, a, b, c, and d are coefficients, and m and n are constants. Your goal is to solve for the variables x and y. To do this, we'll use determinants.

The Code Breakdown

Let’s dive into the code you provided and explain how it works.

Step 1: Calculating the Determinant of a 2x2 Matrix

The determinant of a 2x2 matrix is calculated using the formula:

det = (a * d) - (b * c)

In the code, this is implemented as:

def det2(a,b,c,d){

  return a*d−b*c;

}

Copy above code and go to the Factory page in the Function Calculator and click the menu button on the upper right corner and paste the code into the code editor. 

After that click 'run' button to execute the code. You can follow this process whenever you create a function. If you want to save the functions that you created click 'save'  button for later use. But once a function has been saved you can not create a function with same function signature which is kind of function id. Function signature is determined with two factors, name and parameter count.

This function takes four inputs (a, b, c, d) and returns the determinant of the matrix. Determinants are crucial for solving systems of linear equations.

Step 2: Solving for X and Y

To solve for x and y, we use Cramer's Rule. This involves calculating two new determinants (detX and detY) based on the original matrix but replacing certain columns with constants (m and n).

Solving for X:

def solveX2(a,b,c,d,m,n){

  var det=det2(a,b,c,d);

  if(det==0){

    return -515151;

  }

  var detX=det2(m,b,n,d);

  return detX/det;

}

Here:

• We calculate the determinant of the original matrix (det).

• If det == 0, it means the system has no unique solution.

• Otherwise, we calculate detX by replacing the first column (a and c) with constants (m and n) and solve for x.

Solving for Y:

def solveY2(a,b,c,d,m,n){

  var det=det2(a,b,c,d);

  if(det==0){

    return -515151;

  }

  var detY=det2(a,m,c,n);

  return detY/det;

}

Similarly:

• We calculate detY by replacing the second column (b and d) with constants (m and n) to solve for y.

Step 3: Generalizing the Solution

To make it easier to use these functions in your calculator, we combine them into a single function called solve2. This function allows you to specify which variable (x or y) you want to solve for by passing an additional parameter (xy).

def solve2(a,b,m,c,d,n,xy){

  if(xy==1){

    return solveX2(a,b,c,d,m,n);

  }

  else{

    return solveY2(a,b,c,d,m,n);

  }

}

Step 4: Adding a Custom Function Name

Finally, you’ve defined a custom function name in your calculator's language:

Below is an Korean name example.

def 이원연립해(a,b,m,c,d,n,xy)=solve2(a,b,m,c,d,n,xy)

This is essentially an alias that maps to the main function. In this case:

• 이원연립해 (Korean for "solution to a system of two equations") becomes your custom function name.

• It takes the same parameters as solve2.

How to Use These Functions in Your Calculator

Here’s how you can use these functions step by step:

1. Input Coefficients and Constants: Provide values for a, b, c, d, m, and n.

• Example: Solve the system

• 2x + 3y = 5       4x + y = 6

• a = 2, b = 3, m = 5,

  c = 4, d = 1 (coefficient of y), n = 6.

2. Choose Variable: Decide whether you want to solve for x or y.

   • Pass xy=1 to solve for x.

   • Pass any other value (e.g., xy=0) to solve for y.

3. Run the Function: Call your custom function with these inputs.

4. Solve for x : solve2(2,3,5,4,1,6,1)  

5. Solve for y: solve2(2,3,5,4,1,6,-1) 

6. 
   

7. Interpret Results:

8. • If the result is -515151, it means there’s no unique solution.

   • Otherwise, you'll get the value of either x or y.

   • 
     
     
     

Why Use Custom Functions?

Custom functions like this make solving repetitive math problems quick and easy. Instead of manually calculating determinants or solving equations step by step every time:

• You can automate these calculations.

• • Reduce errors.

  • Save time!

  Conclusion

  With just a few lines of code like the ones above, you've turned your calculator into a powerful tool capable of solving systems of linear equations effortlessly. Whether you're a student or just someone who loves math challenges—this is an excellent way to boost productivity.

  If you have any questions or need further clarification on implementing this code in your calculator setup—feel free to reach out! Happy calculating! 😊