Question

What are Linear Equations in Two Variables?
Explain with an example and its solution.

Answer 1

If a, b, and c are real numbers (and if a and b are not both equal to 0) then ax + by = c is called a linear equation in two variables.

(The “two variables” are the x and the y.) The numbers a and b are called the coefficients of the equation ax + by = c. The number c is called the constant of the equation ax + by = c.

Examples. 3x + 4y = 5 and 4x + 7y = 3 are linear equations in two  variables .

A solution of a linear equation in two variables ax + by = c is a specific point in the Cartesian plane such that when the x-coordinate of the point is multiplied by a, and the y-coordinate of the point is multiplied by b, and those two numbers are added together, the answer equals c.

NOTE : There are always infinitely many solutions to a linear equation in two variables.

Lets taken an example 3x + 4y  =5 

take x = 1 then the value of y can be calculated 

as y = 5 -3x/3 = 5 - 3(1)/3 = 2/3 

The point x = 1 and y = 2/3 is a solution 

but x = 2 and y = -5 is not solution because by putting the values of x and y we don't get the answer = 5