Question

Find c,if the system : cx 3y (3-c)=0 and 12x cy-c=0,has infenetly many solutions

Answer 1

Hey ! You haven't put the signs of the numbers!

Please refer to the attachment. I have given them adequate signs.

Answer 2

Answer:

c = 6

Step-by-step explanation:

Given System of equations are

-cx + 3y + ( 3 - c ) = 0    and  12x - cy - c = 0

To find: Value of c when system of equation has infinitely many solution

Condition for infinitely many solution is given by,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

From given system of equation,

$a_1=-c\:,\:b_1=3\:,\:c_1=3-c\:\:and\:\:a_2=12\:,\:b_2=-c\:,\:c_2=-c$

Putting these value in condition we get,

$\frac{-c}{12}=\frac{3}{-c}=\frac{3-c}{-c}$

to find value of c

consider first equality.i.e.,

$\frac{-c}{12}=\frac{3}{-c}$

$(-c)\times(-c)=3\times12$

$c^2=36$

c = ± √36

c = ± 6

here c = -6 is rejected as it does not satisfy the 2nd equality.

Therefore, c = 6