Q. 45.0( 1 Vote )

Solve the following equations by graphical method- x + y = 4

2x – 3y = 3

Answer :

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

We have the equations,


x + y = 4 …(i)


2x – 3y = 3 …(ii)


Take equation (i), we have


x + y = 4


We can write it as,


x = (4 – y) …(iii)


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 at least three values.


For equation (iii):


Say, we put y = 0.


Then, x = 4 – 0


x = 4


We have, (4, 0).


Now, put y = 1.


Then, x = 4 – 1


x = 3


We have, (3, 1).


Now, put y = 2.


Then, x = 4 – 2


x = 2


We have, (2, 2).


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


Record it in a table,



Now, take equation (ii),


2x – 3y = 3


We can write it as,


2x = 3y + 3



…(iv)


Assign values for y and compute x.


For equation (iv):


Say, we put y = 0.


Then,




x = 1.5


We have, (1.5, 0).


Now, put y = 1.


Then,



x = 3


We have, (3, 1).


Now, put y = 2.


Then,



x = 3 × 2


x = 6


We have, (6, 2).


Record it in a table,



Represent the two tables on a graph, we get



Notice the intersection point of these two lines, x + y = 4 and 2x – 3y = 3.


These two lines intersect each other at (3, 1).


(3, 1) is the solution of these equations.


Thus, solution is x = 3 and y = 1.


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