Determine the value of 'a' for which the following system of linear equation has infinitely many solutions: ax+3y=a-3 ; 12x+ay=a - Maths - Pair of Linear Equations in Two Variables

Question

Determine the value of 'a' for which the following system of
linear equation has infinitely many solutions: ax+3y=a-3 ;
12x+ay=a

Samridhi Sharma · Accepted Answer

ax + 3y = a-3 12x + ay = a
For infinite solutions-----
a/12 = 3/a = (a-3)/a
Case i
a/12 = 3/a
= a^2 = 36
a= either 6 or -6
Case ii
3/a = (a-3)/a
=3a= a^2 - 3a
6a = a^2
i e a can either be 0 or 6
As 6 satisfies both the conditions, hence the value of a is
6