    # Graph Of Linear Equation In Two Variable This is a well-known fact that a linear equation has infinitely many solutions. And the solutions are written as pairs of values.

For example, the solution of the linear equation in two variables x + 2y = 6 can be expressed in the form of a table as given below:

 x 2 0 6 4 ... y 2 3 0 1 ...

On a graph paper these points (2, 2), (0, 3), (6, 0) and (4, 1) are plotted. Now if any two points are joined, a straight line AB is obtained. Hence the geometrical representation of equation x + 2y = 6 is a straight line. All the points which lie on the line AB satisfy the equation x + 2y = 6. For example, if we take points (6, 0), (2, 2) then,

6 + 2(0) = 6 and 2 + 2(2) = 2 + 4 = 6 which means both the points satisfy the equation x + 2y = 6. Hence, (6, 0) and (2, 2) both are solutions of equation x + 2y = 6.

Now if we take a point (2, 0) which does not lie on the line AB then,

2 + 2(0) = 2 ≠ 6, i.e. the point (2, 0) does not satisfy the above equation. Hence, (2, 0) is not a solution.

Example 1:

Draw the graph of linear equation x � y = 2.

Solution:

x � y = 2    =>    y = x � 2

Table of Solutions

 x 2 3 y 0 1

Now plotting the points (2, 0) and (3, 1) on the graph paper and joining these with the help of a ruler we get the line which is the graph of the equation x � y = 2. Example 2:

If the point (1, 1) lies on the graph of the equation 6x + 2ay = 3a, find the value of a.

Solution:

If the point (1, 1) lies on the graph of the equation 6x + 2ay = 3a, then

 6(1) + 2a(1) = 3a => 6 + 2a = 3a => 3a � 2a = 6 => a = 6      (Answer)

Example 3:

Draw the graph of equation 2x + 5y = 13 and check whether x = 2, y = 5 is a solution.

Solution:

 2x + 5y = 13 => 5y = 13 � 2x => y = (13 - 2x)             5
Table of Solutions

 x -1 4 y 3 1

Now plotting the points (-1, 3) and (4, 1) on the graph paper and joining these with the help of a ruler we get the line which is the graph of the equation 2x + 5y = 13. In the above representation, we can clearly see that the point (2, 5) does not lie on the graph and hence x = 2, y = 5 is not a solution of the given equation.

Online Solution Graph of Linear Equation In Two Variable Help:

If you are stuck with a Solution Graph of Linear Equation In Two Variable Homework problem and need help, we have excellent tutors who can provide you with Homework Help. Our tutors who provide Solution Graph of Linear Equation In Two Variable help are highly qualified. Our tutors have many years of industry experience and have had years of experience providing Solution Graph of Linear Equation In Two Variable Homework Help. Please do send us the Solution Graph of Linear Equation In Two Variable problems on which you need Help and we will forward then to our tutors for review.

Online Tutor Solution Graph of Linear Equation In Two Variable:

We have the best tutors in math in the industry. Our tutors can break down a complex Solution Graph of Linear Equation In Two Variable problem into its sub parts and explain to you in detail how each step is performed. This approach of breaking down a problem has been appreciated by majority of our students for learning Solution Graph of Linear Equation In Two Variable concepts. You will get one-to-one personalized attention through our online tutoring which will make learning fun and easy. Our tutors are highly qualified and hold advanced degrees. Please do send us a request for Solution Graph of Linear Equation In Two Variable tutoring and experience the quality yourself.

Other topics under Linear Equations:       • 