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Question

The pair of equations 5x-15y=8 and 3x-9y=245 has,


A

One solution

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B

Two solutions

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C

Infinitely many solutions

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D

no solution

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Solution

The correct option is C

Infinitely many solutions


The explanation for the correct option.

If the equation of two lines are,

a1x+b1y+c1=0a2x+b2y+c2=0

  • If a1a2=b1b2c1c2, the two lines are parallel and have no solutions.
  • If a1a2=b1b2=c1c2, the two lines are coincident and have infinite solutions.
  • If a1a2b1b2, the two lines are intersecting and have unique solutions.

The pair of equations are 5x-15y=8 and 3x-9y=245.

Compared with the standard form,

a1=5,b1=-15,c1=8a2=3,b2=-9,c2=245

a1a2=53b1b2=-15-9=53c1c2=824/5=53

Thus,a1a2=b1b2=c1c2.

Therefore, the given pair of equations has infinite solutions.

Hence, the option (C) is correct.


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