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Question

Which of the following represents a pair of dependent equations?


  1. 5x=63y; 9y=1215x

  2. 3x=63y; 10y=1215x

  3. y=32x2; x=32y

  4. y=27x7; x=27y7


Solution

The correct option is C

y=32x2; x=32y


Consider a pair of linear equations
a1x+b1y+c1=0 and a2x+b2y+c2=0
The equations are said to be dependent if a1a2=b1b2=c1c2 ...(i)

Consider the following equations  
y=32x2; x=32y
By writing them in the standard form, we get 
x2+y+32=0 
x+2y+3=0

Here, a1=12, b1=1 and c1=32
Similarly, a2=1, b2=2 and c2=3

On substituting these values in eq. (i), we get
121=12=323 

Thus, the condition for dependent lines is satisfied.
Hence,the equations y=32x2;x=32y are dependent.

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