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Linear Equation in Two Variables

It is an equation of the form ax + by + c = 0, where a and b are real numbers, a ¹ 0, b ¹ 0 and c are constants (real numbers) and x, y are variables.
 


Let us look at the following linear equation in 2 variables

 1) x + 2y = 3,   

Here x + 2y = 3 can be written as 

 x + 2y - 3 = 0. Here it is in the form ax + by + c = 0 where a =1, b =2 and c = -3

 
2) 2x - 3y - 5 = 0

It is in the form ax + by + c = 0 where a =2, b =-3 and c = -5


3)  5x+7y = 4,

Here 5x + 7y = 4 can be written as

5 x + 7y - 4 = 0

It is in the form ax + by + c = 0 where a =5, b =7and c = -4


Solution 
A pair of values of x and y satisfying the equation ax + by + c = 0 is known as the solution of the equation.

 

Example : x = 1, y = 2 is a solution of x + 3y = 7.

 





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