Q .3. - Calculus

Question

What is a linear equation in three variables? Give an example. What is the graph of a linear equation in three variables? 

Step-by-Step Solution

Answer

$Ax+By+Cz=D\text{ where }A,B,C,D\text{ constants; }2x+4y-7z=2;\text{ plane . }$

Step 1:Given information

A linear equation in three variables 

Step 2:Explaination

A linear equation is an algebraic equation in which each term is either a constant or the product of constant and a variable of exponent one.

An equation of the form$Ax+By+Cz=D$ is called a linear equation in three variables, where $A,B,C D$ are scalars.

 An Example of an equation in three variables is $2x+4y-7z=2$ 

Each linear equation which has three variables determines a plane in three - dimensional space.

Thus the graph of a linear equation in three variables represents a plane.

Hence, the answer is,

$Ax+By+Cz=D\text{ where }A,B,C,D\text{ constants; }2x+4y-7z=2;\text{ plane . }$