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Q.

Find whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident with the help of a graph.

3x−4y−1=0,2x− 8 3 y−4=0  

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a

Coincident

b

Intersecting

c

Parallel

d

None of the above 

answer is C.

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Detailed Solution

The given equations are 3x−4y−1=0   and 2x− 8 3 y−4=0  .
For the line equation 3x−4y−1=0  ,
Putting x=0   in the equation 3x−4y−1=0  ,
⇒3x−4y−1=0 ⇒3(0)−4y−1=0 ⇒4y=−1 ⇒y=− 1 4  
Putting y=0   in the equation 3x−4y−1=0   to obtain the value of x  ,
⇒3x−4(0)−1=0 ⇒3x=1 ⇒x= 1 3  
So, the coordinates of the line equation 3x−4y−1=0   are 0,− 1 4   and 1 3 ,0  .
For the second line equation 2x− 8 3 y−4=0  ,
Putting x=0   in the equation 2x− 8 3 y−4=0   to obtain the value of y  ,
⇒2x− 8 3 y−4=0 ⇒2(0)− 8 3 y−4=0 ⇒ 8 3 y=−4 ⇒y= −12 8 ⇒y=−1.5  
Putting y=0   in the equation 2x− 8 3 y−4=0  ,
⇒2x− 8 3 y−4=0 ⇒2x− 8 3 (0)−4=0 ⇒2x=4 ⇒x= 4 2 ⇒y=2  
So, the coordinates of the line equation 2x− 8 3 y−4=0   are 0,−1.5   and 2,0  .
Plot the graph of the line 3x−4y−1=0   using the table below:

x

0

1 3  

y

− 1 4  

0

And, plot the graph of the line 2x− 8 3 y−4=0   using the table below:

X

0

2

Y

-1.5

0

The graph of the lines is represented as,
Question ImageFrom the graph, we can see that the two lines are parallel.
Hence, the correct option is 3.
 
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