Understanding Linear Algebra Systems | Maths Explanation for Java Kids
Welcome to this beginner-friendly Java tutorial designed for junior secondary students learning algebra.
Java is a great tool for solving math problems. It helps students visualize and automate algebraic solutions. This tutorial is perfect for:
- Junior secondary students learning Java
- Teachers looking for math coding projects
- Anyone curious about solving equations with code
In this lesson, you'll discover how to solve simultaneous equations with two unknowns using Java.
We'll walk through the elimination method and show you how to write a simple Java script to solve linear systems.
The resulting algorithm solves the linear system using basic algebra and Java logic.
It's ideal for school projects and math exercises.
Well, it hasn't been much of algebra in our junior secondary school Java tutorial series so far; We are about to have our first taste of it.
What Are Simultaneous Equations? | Maths Explanation for Java Kids
Simultaneous equations are a set of equations with multiple variables that are solved together. For example:
2x + 3y = 13; and
5x - y = 7
Simultaneous equations can be solved using algebraic methods like Substitution or Elimination,
or advanced methods like Matrix and Cramer's Rule.
In this tutorial, we'll focus on the elimination method and implement it using Java.
Step-by-Step Guide to Solve Simultaneous Equations with 2 Unknowns | Elimination Method Java Algorithm
Let's try to draft a Java algorithm that solves simultaneous equations with 2 unknowns,
using the elimination method, with the following set of equations in consideration.
2x + 3y = 13; and
5x - y = 7
Step 1:
Pick a variable to eliminate, either x or y.
Our code will always eliminate the y variable.
Step 2:
Multiply equation 1 by the coefficient of variable y
in equation 2.
⇒
-1 X (2x + 3y = 13)
⇒
-2x - 3y = -13
Step 3:
Multiply equation 2 by the coefficient of variable y
in equation 1.
⇒
3 X (5x - y = 7)
⇒
15x - 3y = 21
Step 4:
Subtract the new equations obtained from Steps 2 and 3.
-2x - 3y = -13
-
15x - 3y = 21
⇒
-17x = -34
Step 5:
Divide the R.H.S. from Step 4 by the coefficient of
x to obtain x.
⇒
x = -34/-17 = 2;
Step 6:
Obtain y by solving for y from any of the
original equations, using the found value of x.
2x + 3y = 13
⇒
2(2) + 3y = 13;
⇒
3y = 13 - 4 = 9;
⇒
y = 9/3 = 3;
Create a new Java class file;
call it Simultaneous2Unknown.
Type out the adjoining Java code for solving simultaneous equations with 2 unknowns.
Note: You can comment out the SortFraction Java object
code in the main class from the previous lesson or simply continue from where it stopped.
So! Java Fun Practice Exercise - Simultaneous Equations with 2 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 Java code solves the resulting 2 by 2 Simultaneous Equations.
Java Code for Solving Simultaneous Equations with 2 Unknowns - Class File
package algebra;
public class Simultaneous2Unknown {
private final double[] x_coefficients;
private final double[] y_coefficients;
private final double[] equals;
private final double[][] eliminator;
private double x_variable;
private double y_variable;
public Simultaneous2Unknown(double[] x_coeff, double[] y_coeff, double[] eq) {
x_coefficients = new double[]{x_coeff[0], x_coeff[1]};
y_coefficients = new double[]{y_coeff[0], y_coeff[1]};
equals = new double[]{eq[0], eq[1]};
eliminator = new double[2][2];
}
public double[] solveSimultaneous() {
eliminator[0][0] = y_coefficients[1] * x_coefficients[0];
eliminator[0][1] = y_coefficients[1] * equals[0];
eliminator[1][0] = y_coefficients[0] * x_coefficients[1];
eliminator[1][1] = y_coefficients[0] * equals[1];
try {
x_variable = (double)(eliminator[0][1] - eliminator[1][1]) / (eliminator[0][0] - eliminator[1][0]);
y_variable = (double)(equals[0] - x_coefficients[0] * x_variable) / y_coefficients[0];
} catch (ArithmeticException e) {
throw e;
}
return new double[]{x_variable, y_variable};
}
}
Java Code for Solving Simultaneous Equations with 2 Unknowns - Main Class
package algebra;
public class Algebra {
public static void main(String[] args) {
System.out.println("Welcome to our demonstration sequels");
System.out.println("Hope you enjoy (and follow) the lessons.");
System.out.println("");
char[] operator = new char[]{'+', '+'};
double[] result2D;
double[] x_coeff = new double[]{1, -2};
double[] y_coeff = new double[]{1, 1};
double[] equals = new double[]{2, -1};
if (y_coeff[0] < 0) {
operator[0] = '-';
}
if (y_coeff[1] < 0) {
operator[1] = '-';
}
System.out.println("Solving simultaneously the equations:");
System.out.printf("%40s%.2fx %s %.2fy = %.2f%n", "", x_coeff[0],
operator[0], Math.abs(y_coeff[0]), equals[0]);
System.out.printf("%40s%.2fx %s %.2fy = %.2f%n", "", x_coeff[1],
operator[1], Math.abs(y_coeff[1]), equals[1]);
System.out.printf("%n%30s%n%40s", "Yields:", "(x, y) = ");
try {
Simultaneous2Unknown sim2unk;
sim2unk = new Simultaneous2Unknown(x_coeff, y_coeff, equals);
result2D = sim2unk.solveSimultaneous();
System.out.printf("(%.4f, %.4f)%n", result2D[0], result2D[1]);
} catch (ArithmeticException e) {
System.out.printf("(%s, %s)%n", "∞", "∞");
}
System.out.println("\n\n");
}
}
