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
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.:
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
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
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.