This question was previously asked in

UP TGT Mathematics 2016 Official Paper

- no common solution
- exactly one common solution
- exactly two common solution
- more than two common solutions

Option 4 : more than two common solutions

Free

CT 1: हिन्दी (आदिकाल)

5586

10 Questions
40 Marks
10 Mins

**Concept:**

If two linear equations

a_{1}x + b_{1}y = c_{1} and a_{2}x + b_{2}y = c_{2}. Then,

(a) If a_{1}/a_{2 }= b_{1}/b_{2 }= c_{1}/c_{2 }, the system is consistent and has infinitely many solutions.

(b) If a_{1}/a_{2 }= b_{1}/b_{2 }≠ c_{1}/c_{2 }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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