Question

Q6 For what value of a, the system
of equations
ax+3y=a-3, 12x+ay=a will have no
solution?
​

Answer 1

Answer:

a = -6

Step-by-step explanation:

Given a pair of linear equations such that,

ax + 3y = a-3

12x + ay = a

To find the value of a for which it has no solution.

We know that,

For a pair of linear equations,

A1x + B1y = C1

A2x + B2y = C2

There will be no solution iff,

• A1/A2 = B1/B2 ≠ C1/C2

Here, we will get,

=> a/12 = 3/a ≠ (a-3)/a

Therefore, we will get,

=> a×a = 12×3

=> a^2 = 36

=> a = ±6

And,

=> 3a ≠ a(a-3)

=> 3a ≠ a^2 - 3a

=> a^2 -6a ≠ 0

=> a(a-6) ≠0

=> a ≠0 and a≠6

Hence, the required value of a = -6.