Question : Find 'c' if the system of linear equations cx+3y+(3-c)=0; 12x+cy-c=0 has infinitely many solutions.
Doubt by Mehak
Solution :
cx+3y+(3-c)=0
12x+cy-c=0
For infinitely many salutations
a1/a2 = b1/b2 = c1/c2
c/12 = 3/c = (3-c)/(-c)
c/12 = 3/c
c² = 12×3
c² = 36
c=±6 — (1)
Also,
3/c = (3-c)/(-c)
-3c = 3c-c²
c²-3c-3c=0
c²-6c=0
c(c-6)=0
c=0 & c-6=0
c=0 & c=6 — (2)
From equations (1) & (2)
c = 6