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

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 =

If  c = -2 then;

(-2)² = 4 = , 4x - 4 = 36x , 32x = -4 , x =

If c = 2  then;

2² =

If c = 6 then;

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

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

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

answer: i ! the answer is   9000 seconds, also d

hope i

-lavira : )