Question

Determine the value of a for which the following system of linear equation has an infinite number of solutions:Ax+3y=a–312x+ay=a​

Answer 1

Answer:

a = -6

Step-by-step explanation:

for what value of a, the pair if linear equation. ax+3y=a-3,12x+ay=a has no solutions?

ax + 3y = a-3

12x + ay = a

these Lines will not have any solutions if lines are parallel and are at an distance

so slope of line will be same and c will differ

y = mx + c

so writing given equations in this form

so y = (-a/3)x + (a-3)/3   - Eq 1

    y = (-12/a)x  + 1    - Eq 2

Equating m from Eq 1 & Eq 2

=> -a/3 = -12/a

=> a² = 36

=> a = ±6

Not Equating c from Eq 1 & Eq 2

(a-3)/3 ≠ 1

=> a -3 ≠ 3

=> a ≠ 6

so a = 6 is eliminated ( for a = 6 there will be infinite solution has both equations will be of same line)

As out of ±6 , +6 is eliminated Hence only value of a= -6 for which no solutions

a = - 6