Systems of Linear Equations in Three Variables

Systems of Linear Equations in Three Variables

3.1

Systems of Linear Equations in Three Variables

Definition

Two or more linear equations involving the same set of variables form a system of linear equations.

Visual representation of characteristics of systems of linear equations in three variables

Example

\(4x-2y+z=2\)

\(6x+7y-z=3\)

\(5x+y+2z=7\)

Form in Cartesian Plane

Geometrically, a linear equation in three variables forms a plane in a three-dimensional space.

Triangular plane formed by three points and connecting lines.

Type of Solution	Description
One Solution	The planes intersect at only one point
Infinite Solutions	The planes intersect in a straight line
No Solution	The planes do not intersect at any point

Methods used to solve systems of linear equations in three variables

Elimination Method
Substitution Method

Systems of Linear Equations in Three Variables

3.1

Systems of Linear Equations in Three Variables

Definition

Two or more linear equations involving the same set of variables form a system of linear equations.

Visual representation of characteristics of systems of linear equations in three variables

Example

\(4x-2y+z=2\)

\(6x+7y-z=3\)

\(5x+y+2z=7\)

Form in Cartesian Plane

Geometrically, a linear equation in three variables forms a plane in a three-dimensional space.

Triangular plane formed by three points and connecting lines.

Type of Solution	Description
One Solution	The planes intersect at only one point
Infinite Solutions	The planes intersect in a straight line
No Solution	The planes do not intersect at any point

Methods used to solve systems of linear equations in three variables

Elimination Method
Substitution Method