Solving Simultaneous Equations With 3 Unknowns in JavaScript

Solving Simultaneous Equations in JavaScript: A Junior Secondary Guide

Welcome to this junior secondary JavaScript math project! In this tutorial, you'll learn how to solve simultaneous equations with three unknowns using JavaScript. This is a great way to combine your coding skills with algebra and logic.
You'll also learn the following:

How to use JavaScript to solve 3x3 simultaneous equations
Applying the elimination method step-by-step
Using LCM (Least Common Multiple) to simplify equations
Writing a JavaScript class to automate the solving process

Solving equations is a key part of algebra. By coding the solution in JavaScript, you'll not only understand the math better; you'll also build a useful tool. This project is perfect for students looking to explore JavaScript math algorithms, or teachers seeking JavaScript algebra exercises for the classroom.

How to Solve Three-Variable Algebra Problems | Maths Explanation for JavaScript Kids

To solve 3 by 3 simultaneous equations, we will simply eliminate the z variable, then call out to our JavaScript Code for Simultaneous Equations with 2 Unknowns module.

Step-by-Step Guide to Solve Three-Variable Algebra Equations | Elimination Method JavaScript Algorithm

Let's try to draft a JavaScript algorithm that solves simultaneous equations with 2 unknowns, using the elimination method, with the following set of equations in consideration.
         x + 2y - z = 2; and
         3x - y + 2z = 4
         2x + 3y + 4z = 9
These steps will help the student understand both the math and the logic behind the code.

Step 1:

Using the Find LCM in JavaScript class from the Primary Category, find the LCM of the coefficients of variable z. Multiply equations 1, 2 & 3 by the LCM of the coefficients of variable z, divided by the z coefficient of the respective equation.
         (⁴/_-1) X (x + 2y - z = 2)
    ⇒     -4x - 8y + 4z = -8
         (⁴/₂) X (3x - y + 2z = 4)
    ⇒     6x - 2y + 4z = 8
         (⁴/₄) X (2x + 3y + 4z = 9)
    ⇒     2x + 3y + 4z = 9

Step 2:

Subtract the new equations obtained in Step 2; eqn (2) from eqn (1) and eqn (3) from eqn (2).
         -4x - 8y + 4z = -8
    -     6x - 2y + 4z = 8
    ⇒     -10x - 6y = -16
         6x - 2y + 4z = 8
    -     2x + 3y + 4z = 9     ⇒     4x - 5y = -1

Step 3:

Call out to our JavaScript Code for Simultaneous Equations with 2 Unknowns module to solve for x and y.
⇒ (x, y) = (1, 1);

Step 4:

Obtain z by solving for z from any of the original equations, using the found values of x and y.
         x + 2y - z = 2
⇒         1 + 2(1) - z = 2;
⇒         -z = 2 - 3 = -1;
⇒         z = ^-1/_-1 = 1;

Create 2 new files; On Notepad++: File, New.
Call them Simultaneous3Unknown.html and Simultaneous3Unknown.js;
Type out the adjoining JavaScript code for solving simultaneous equations with 3 unknowns.
.

Note: The code module for finding LCM in JavaScript has been explained in the Primary Category.

So! JavaScript Fun Practice Exercise - Simultaneous Equations with 3 Unknowns

As a fun practice exercise, feel free to try out your own set of x_coefficients, y_coefficients and equals values, and see how the JavaScript code solves the resulting 3x3 Simultaneous Equations.

JavaScript Code for Simultaneous3Unknown.html

<!DOCTYPE html>
<html lang="en">
    <head>
        <title>Three Dimensional Simultaneous Equation</title>
        <script src="LCM.js"></script>
        <script src="Simultaneous2Unknown.js"></script>
        <script src="Simultaneous3Unknown.js"></script>
    </head>
    <body>

        <h3>3 Dimensional Simultaneous Equation</h3>
        
        <div id="three_dim"></div>

        <script>

            var operator = [];
            operator[0] = ['+', '+'];
            operator[1] = ['+', '+'];
            operator[2] = ['+', '+'];
            for (var i = 0; i < 3; i++) {
                if (y_3coeff[i] < 0) {
                    operator[i][0] = '-';
                }
                if (z_3coeff[i] < 0) {
                    operator[i][1] = '-';
                }
            }
            var result = "Solving simultaneously the equations:<br/>";

            //Print as an equation
            result += x_3coeff[0] + "x   " + operator[0][0] +
                    "   " + Math.abs(y_3coeff[0]) + "y   " +
                    operator[0][1] + "   " + Math.abs(z_3coeff[0]) +
                    "z   =   " + eq_3coeff[0] + "<br/>";

            result += x_3coeff[1] + "x   " + operator[1][0] +
                    "   " + Math.abs(y_3coeff[1]) + "y   " +
                    operator[1][1] + "   " + Math.abs(z_3coeff[1]) +
                    "z   =   " + eq_3coeff[1] + "<br/>";

            result += x_3coeff[2] + "x   " + operator[2][0] +
                    "   " + Math.abs(y_3coeff[2]) + "y   " +
                    operator[2][1] + "   " + Math.abs(z_3coeff[2]) +
                    "z   =   " + eq_3coeff[2] + "<br/>";
            result += "Yields: <br/>";

            result += "(x,   y,   z)   =   ";

            try {
                // Solve simultaneously
                solveSimultaneous3D();
                result += "(" + x_variable + ",   " + y_variable +
                        ",   " + z_variable + ")";
            } catch (ex) {
                result += "(∞,   ∞,   ∞)";
            }
            document.getElementById("three_dim").innerHTML = result;

        </script>

    </body>
</html>

JavaScript Code for Simultaneous3Unknown.js

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