Answer:
6
Step-by-step 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
Answer:
6
Step-by-step 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 = [tex]\frac{36x}{x - 1}[/tex]
If c = -2 then;
(-2)² = 4 = [tex]\frac{36x}{x - 1}[/tex] , 4x - 4 = 36x , 32x = -4 , x = [tex]-\frac{1}{8}[/tex]
If c = 2 then;
2² = [tex]4 = \frac{36x}{x - 1} , 4x - 4 = 36x , 32x = -4 , x = -\frac{1}{8}[/tex]
If c = 6 then;
6² = 36 = [tex]\frac{36x}{x - 1}[/tex] , 36x - 36 = 36x, 36x - 36x = 36 , x (36 - 36) = 36 , x(0) = 36 , x = [tex]\frac{36}{0}[/tex] = undefined or infinitely many solutions.
Hence the system of equations given above will have infinitely many solutions if the value of c is 6.
