The equations 3x - 4y = 5 and 12x - 16y = 20 have:

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UP TGT Mathematics 2016 Official Paper
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  1. no common solution
  2. exactly one common solution
  3. exactly two common solution
  4. more than two common solutions

Answer (Detailed Solution Below)

Option 4 : more than two common solutions
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Detailed Solution

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Concept: 

If two linear equations

​x + b1y ​= c1​ and ​x + b2y ​= c2​. Then,

(a) If ​​/a2 = b1​​/b2 ​​= c1​​/c2 ​​, the system is consistent and has infinitely many solutions.

(b) If ​​/a2 = b1​​/b2 ≠ c1​​/c2 the system has no solution and is inconsistent

Calculation:

In equations 3x − 4y = 5 and 12x − 16y = 20

3/12 = -4/-16 = 5/20 ⇒ ¼ = ¼ = ¼

So the system is consistent and has infinitely many solutions 

∴ They have more than two common solutions.

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