Linear Equation Using Two Variables

Prakash1111111

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General form of linear equation using 2 variables I always read can be written:

Code:
Ax + By + C = 0

where A and B cannot both be 0

So does it means like

1x + 0y + c = 0 is a linear equation of two variables i.e basically what I am asking is that both A and B cannot be zero but can either A or B be 0 like :

Code:
0x+4y-5=0

Is the above equation a Linear equation of 2 variables?

Please clarify my doubt .
 
General form of linear equation using 2 variables I always read can be written:
Ax + By + C = 0 where A and B cannot both be 0.
That is correct. The last condition has this mathematical form: \(\displaystyle |A|+|B|\ne 0\).

Thus any of these is a linear equation.
\(\displaystyle \begin{align*}3x-3y+6&=0\\4x+8&= 0\\5y&=-9\\6x-5y&=30 \end{align*}\)
 
So [is] 1x + 0y + c = 0 ... a linear equation of two variables[?]

[Is] 0x + 4y - 5 = 0 ... a Linear equation of 2 variables?

So [can we] write a linear equation of 2 variables like ... 2x + 0y + 3 = 0

Hello Prakash:

I'm thinking that Denis and pka may have misread your questions.

The answer to each of your questions above is "no" because those are all examples of a linear equation in one variable.

In other words, if A is zero and B is not zero, the result is a linear equation in one variable.

If B is zero and A is not zero, the result is a linear equation in one variable.

If both A and B are not zero, the result is a linear equation in two variables.

If both A and B are zero, the result is not a linear equation.

(Source: Introductory Algebra for College Students -- 4th Edition, by Robert Blitzer; pages 103, 213)

Cheers :cool:
 
I'm thinking that Denis and pka may have misread your questions.
The answer to each of your questions above is "no" because those are all examples of a linear equation in one variable.
That is wrong. If one is working with linear equations of two variables, one must account for both vertical lines \(\displaystyle 0x+By+C=0\) and horizontal lines \(\displaystyle Ax+0y+C=0\) where \(\displaystyle |A|\cdot |B|\ne 0\). Therefore both of those are forms are members of the two dimensional linear space of linear equations.

BTW. Robert Blitzer is not listed at the site of mathematicians.
 
Last edited:
Hello Prakash:

I'm thinking that Denis and pka may have misread your questions.

The answer to each of your questions above is "no" because those are all examples of a linear equation in one variable.

In other words, if A is zero and B is not zero, the result is a linear equation in one variable.

If B is zero and A is not zero, the result is a linear equation in one variable.

If both A and B are not zero, the result is a linear equation in two variables.

If both A and B are zero, the result is not a linear equation.

(Source: Introductory Algebra for College Students -- 4th Edition, by Robert Blitzer; pages 103, 213)

Cheers :cool:


I too disagree with what you are saying. How can a line be drawn in the x-y plane and not have two variables?
 
both of those are forms are members of the two dimensional linear space of linear equations

This explanation is not appropriate, on the beginning-algebra board.
 
This explanation is not appropriate, on the beginning-algebra board.
May I respectfully ask how you would know? After all, you did quote from a textbook not widely respected.
 
This example cleared all my doubts :

Assume that the number of girls and boys in a classroom is represented using a system of linear equations of two variables. If there are a total of 30 students in the classroom and if there are 10 more boys than girls, we can write this equation using two variables as:
Code:
[I]
g[/I] + [I]b[/I] = 30 

[I]g[/I] + 10 = [I]b[/I]

The first equation tells us that when we add the number of girls, g, and the number of boys, b, together, we get a total of 30 students in the classroom. The second equation tells us that the number of boys is 10 more than the number of girls.

Now based upon my original question - either boys or girls would be total 0 - equation could now be changed to twice the number of girls in class added to 10 would be 30

Code:
2g + 10 = 30

that is it would mean that number of boys are 0 - hence even if the above equation is a linear equation of one variable but we can represent it as linear equation of two variables but the variables values in all should be 0 i.e.:

Code:
2g + 3b + 10 = 30

where b = 0

So in all as per my question - if A or B is zero indeed the equation would be a linear equation of one variables and we can granted take that all other variables in it is constant value 0. The reason to consider this scenario is when I draw a graph of equation

Code:
x = 3

The values of y can be 1,2,3,4,5, ......... [parallel line to Y axis] for a line passing through x at 3 which would then mean equation as

Code:
x + 0.y = 3

Hence please correct me in finally stating that

In a linear equation of 2 variables

Code:
Ax + 0y + c = 0
0x + By + c = 0

A or B can be zero but not both of them and that it would no more be a linear equation of two variables rather would now become a linear equation of one variable and the value of other variables would be multiplied with a constant 0.
 
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