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.
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.
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
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 |
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.
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.
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