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
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
<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>
<!-- This is where the result will be displayed when it is ready.-->
<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
var x_3coeff = [2, 4, 2];
var y_3coeff = [1, -1, 3];
var z_3coeff = [1, -2, -8];
var eq_3coeff = [4, 1, -3];
eliminator = [];
eliminator[0] = [];
eliminator[1] = [];
eliminator[2] = [];
var z_variable;
x_2coeff = [];
y_2coeff = [];
eq_2coeff = [];
function solveSimultaneous3D() {
var lcm;
// find the LCM z coefficients
lcm = getLCM([Math.abs(z_3coeff[0]), Math.abs(z_3coeff[1]), Math.abs(z_3coeff[2])]);
// STEP 1:
eliminator[0][0] = (lcm * x_3coeff[0]) / z_3coeff[0];
eliminator[0][1] = (lcm * y_3coeff[0]) / z_3coeff[0];
eliminator[0][2] = (lcm * eq_3coeff[0]) / z_3coeff[0];
eliminator[1][0] = (lcm * x_3coeff[1]) / z_3coeff[1];
eliminator[1][1] = (lcm * y_3coeff[1]) / z_3coeff[1];
eliminator[1][2] = (lcm * eq_3coeff[1]) / z_3coeff[1];
eliminator[2][0] = (lcm * x_3coeff[2]) / z_3coeff[2];
eliminator[2][1] = (lcm * y_3coeff[2]) / z_3coeff[2];
eliminator[2][2] = (lcm * eq_3coeff[2]) / z_3coeff[2];
// STEP 2:
x_2coeff = [
eliminator[0][0] - eliminator[1][0],
eliminator[1][0] - eliminator[2][0]
];
y_2coeff = [
eliminator[0][1] - eliminator[1][1],
eliminator[1][1] - eliminator[2][1]
];
eq_2coeff = [
eliminator[0][2] - eliminator[1][2],
eliminator[1][2] - eliminator[2][2]
];
try {
// STEP 3:
solveSimultaneous2D();
// STEP 4:
z_variable = (eq_3coeff[0] - x_3coeff[0] * x_variable -
y_3coeff[0] * y_variable) / z_3coeff[0];
} catch (ex) {
throw ex;
}
}