Theory:

"Life is a linear equation in which you can't cross multiply!  
  
If you think you can do it, you can do it. If you think you can't do it, you can't do it. It's a simple formula."
 
~Israelmore Ayivor.
In your previous class, you have studied the linear equation with one variable. Using these equations, you can solve the mathematics problems and our real-life problems as well.
 
But in some circumstances, we ought to use more than one variable in an equation. In this chapter, learn linear equation in two variables.
 
Let's see an example to understand it.
 
In a One-day International Cricket match between India and Australia, two Indian batsmen scored 142 runs together.
 
In this above scenario, we can observe that the score of neither of them is known. So, there are two unknown quantities. Let us take that as \(x\) and \(y\), respectively.
 
Therefore, \(x + y\) \(=\) 142. This is the required linear equation in two variables.
 
To represent the two variables, we can use the other alphabets as well.
Example:
1. \(a + b\) \(= 100\)
 
2. \(20s +10t\) \(= 225\)
 
3. \(0.2p +20.5q\) \(= 332.5\)
 
4. 9=10b40c
What is a linear equation in two variable?
A linear equation in which two variables are involved in which each variable is in the first degree.
 
It can be written in the form of \(ax + by + c = 0\) where \(a\), \(b\) and \(c\) are real numbers, both \(a\) and \(b\) are not both zero, \(x\) and \(y\) are variables, and \(c\) is a constant.
The equation in which two variables involved, each of which is in the first degree. These variables are arranged so that they are not multiplied by each other is called a linear equation in two variables.