Question

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

Short answer

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

Step-by-step solution

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 $A,B,CD$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,

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