Question

The system of equations cx + 3y = c – 3 and 12x + cy = c will have infinitely many solutions if the value of c is

2 points

– 2

2

6

3​

Answer 1

6

Explanation:

The system of equations:

cx + 3y = c - 3 ... (i)

12x + cy = c ... (ii)

Multiplying (i) by c and (ii) by 3 gives;

c²x + 3cy = c² - 3c ... (i)

36x + 3cy = 3c ... (ii)

(i) - (ii) gives;

c²x - 36x + 0 = c² - 3c - 3c

c²x - 36x = c²

c²x - c² = 36x

c²(x - 1) = 36x

c² =
`(36x)/(x - 1)`

If c = -2 then;

(-2)² = 4 =
`(36x)/(x - 1)` , 4x - 4 = 36x , 32x = -4 , x =
`-(1)/(8)`

If c = 2 then;

2² =
`4 = (36x)/(x - 1) , 4x - 4 = 36x , 32x = -4 , x = -(1)/(8)`

If c = 6 then;

6² = 36 =
`(36x)/(x - 1)` , 36x - 36 = 36x, 36x - 36x = 36 , x (36 - 36) = 36 , x(0) = 36 , x =
`(36)/(0)` = undefined or infinitely many solutions.

Hence the system of equations given above will have infinitely many solutions if the value of c is 6.

Answer 2

6

Explanation:

1. re-write the given system:

cx+3y=c-3; => y= -cx/3 +(c-3)/3

12x+cy=c; => y= -12x/c+c/12

2. according the condition the rule for the parallel graphs is:

-c/3= -12/c

3. to calculate the unknown 'c':

c²=36; ⇔c=±6