What value of b will cause the system to have an infinite

number of solutions?

y = 6x-b

3x+1/2y=-3

-3x + 2 y = - 3

b =

O 2

X

04

6

8

6

Step-by-step explanation:

Given the system of equations:

y = 6x-b (eq. 1)

-3x+1/2y = - 3 (eq. 2)

We can rewrite eq. 1 as follows:

-6x + y = - b

Dividing by 2:

(-6x + y) / 2 = - b/2

-6x/2 + y/2 = - b/2

-3x + 1/2y = - b/2

The system of equations will have infinite number of solutions if both equations are equal. Therefore:

-b/2 = - 3

b = - 3 * (-2)

b = 6