untitled

0DWK,;;)RUPD

x 1  2  3 

y 4  0   4 

x  2  0  2 

y 6  3  0 



Example 10. Solv e with the help of graphs : x 8 4 x
2

3

3  

Solution : Given equation is x 8 4 x
2

3

3  

Let, y x 8 4 x
2

3

3  

? .........( 1 )
2

3

y 3  x

And,y 8  4 x..........( 2 )
Now, Taking some values of x in equation (1), we find the
corresponding values of y and make the adjoining
table :
? three points on the graph of the equation (1) are :
( 2 , 6 ),( 0 , 3 ),( 2 , 0 )
Again, taking some values of x in equation (2), we
find the corresponding values of y and make the
adjoining table :
? three points on the graph of the equation (2) are :
( 1 , 4 ),( 2 , 0 ),( 3 , 4 )
Let XOXcandYOYc be x-axis, y-axis respectively
andO, the origin. We take each side of the smallest squares along with both axes as
unit. Now, we plot the points ( 2 , 6 ),( 0 , 3 ),( 2 , 0 ), obtained from equation (1) on the
graph paper and join them each other. The graph is a straight line. In the same way,
we plot the points ( 1 , 4 ),( 2 , 0 ),( 3 , 4 ) obtained from equation (2) and join them each
other. This graph is also a straight line. Let the two straight lines intersect at P. It is
seen from the picture that the coordinates of the point of intersection are ( 2 , 0 ).
? solution is x 2 , or solution is 2

Activity : Find four points on the graph of the equation 2 xy 3 0 in terms of

a table. Then, taking unit of a fixed length on the graph paper, plot the points and

join them each other. Is the graph a straight line?

Exercise 12⋅ 3
Solve by graphs :

1. 3 x 4 y 14 2. 2 xy 1 3. 2 x 5 y 1
   4 x 3 y 2 5 xy 13 x 3 y 2


2. 3 x 2 y 2 5. 2
   2 3



x y

6. 3 xy 6

5 x 3 y 5 2 x 3 y 13 5 x 3 y 12