Sistem Persamaan Linier 3 Variabel

Study Notes

Introduction

A system of linear equations with three variables is a set of three linear equations that involve three variables.
The goal is to find the values of the three variables that satisfy all three equations.

General Form

The general form of a system of linear equations with three variables is:

a1x + b1y + c1z = d1
a2x + b2y + c2z = d2
a3x + b3y + c3z = d3

Where a1, b1, c1, d1, a2, b2, c2, d2, a3, b3, c3, and d3 are constants, and x, y, and z are the variables.

Solution Methods

There are several methods to solve a system of linear equations with three variables, including:
1. Substitution Method: Solve one equation for one variable, and then substitute that expression into the other two equations.
2. Elimination Method: Add or subtract equations to eliminate one variable, and then solve for the remaining variables.
3. Matrix Method: Use matrices to represent the system of equations, and then solve using matrix operations.

Consistency and Independence

A system of linear equations with three variables can be:
- Consistent: Has a unique solution.
- Inconsistent: Has no solution.
- Dependent: Has infinitely many solutions.
The consistency and independence of the system can be determined by finding the rank of the coefficient matrix.

Graphical Representation

A system of linear equations with three variables can be represented graphically in a 3D coordinate system.
Each equation represents a plane in 3D space, and the solution to the system is the point of intersection of the three planes.
If the system is inconsistent, the planes do not intersect. If the system is dependent, the planes intersect in a line or a plane.

Description

Pelajari tentang sistem persamaan linier dengan tiga variabel, termasuk bentuk umum, metode penyelesaian, konsistensi dan independensi, serta representasi grafis. Quiz ini membantu Anda memahami konsep-konsep dasar dalam sistem persamaan linier.