Q. 65.0( 1 Vote )

Solve the following equations by graphical method-3x-4y=1;

Answer :

For solving these equations by the graphical method, we need to form separate tables for each equation.

We have the equations,


3x – 4y = 1 …(i)


…(ii)


Take equation (i), we have


3x – 4y = 1


We can write it as,


3x = 4y + 1



Now, assign values of y and compute values for x.


We can assign values of y = …, -3, -2, -1, 0, 1, 2, 3, 4,…


It is not necessary to put all values. But to form an accurate graph, it is necessary to put atleast three values.


Say, we put y = -3.


Then,




x = -3.67


We have, (-3.67, -3).


Now, put y = -2.


Then,




x = -2.33


We have, (-2.33, -2).


Now, put y = -1.


Then,




x = -0.33


We have, (-0.33, -1).


Now, put y = 0.


Then,




x = 0.33


We have, (0.33, 0).


Now, put y = 1.


Then,




x = 1.67


We have, (1.67, 1).


Now, put y = 2.


Then,




x = 3


We have, (3, 2).


We can further find out x by putting values of y = 3, 4, 5,… but here we have just put six values.


Record it in a table,



Now, take equation (ii),



We can write it as,



-6x + 8y = 15


6x = 8y – 15



Assign values for y and compute x.


Say, we put y = -3.


Then,





x = -6.5


We have, (-6.5, -3).


Now, put y = -2.


Then,




x = -5.167


We have, (-5.167, -2).


Now, put y = -1.


Then,




x = -3.83


We have, (-3.83, -1).


Now, put y = 0.


Then,





x = -2.5


We have, (-2.5, 0).


Now, put y = 1.


Then,




x = -1.167


We have, (-1.167, 1).


Now, put y = 2.


Then,




x = 0.167


We have, (0.167, 2).


Record it in a table,



Represent the two tables on a graph, we get



Notice that, the two lines are inconsistent. It mean that they will meet at a specific point and the point that we did not took in the solution.


That point will be (17/12, 13/16) and can be found that both the lines will intersect at this point.


So point (17/12, 13/16) is the solution to the given equations.


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