Q. 22 A5.0( 2 Votes )

# For what value of a, the following system of linear equations has no solutions:

ax + 3y = a – 2, 12x + ay = a

Answer :

Given, pair of equations

ax + 3y = a – 2

and 12x + ay = a

On comparing the given equation with standard form i.e. a_{1} x + b_{1}y + c_{1} = 0 and a_{2} x + b_{2}y + c_{2} = 0, we get

a_{1} = a, b_{1} = 3 and c_{1} = – (a – 2)

and a_{2 =} 12, b_{2} = a and c_{2} = – a

For no solutions,

∴

On taking I and II terms, we get

⇒ a^{2} = 36

⇒ a = √36

**⇒** **a =** **±****6**

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