What value of b will cause the system to have an infinite number of solutions? y=6x+b -3x+1/2y=-3

b = -6

Step-by-step explanation:

Given:

y=6x+b (eq 1)

and

-3x+1/2y=-3    (Rearrange this equation to look likes eq (1) , add -3x to both sides)

(1/2) y = 3x - 3   (multiply both sides by 2)

y = 2(3x -3)   (distribute the 2 into parentheses)

y = 6x - 6 (eq 2)

Recall that a system of equations will have an infinite number of solutions if both equations are the same line.  (i.e they have the same slope and y intercept)

In our case, if you compare eq 1 and eq 2, the way to make both equations the same line is if b = -6. (this is the answer)

1: -2 3/4, -2 1/2, -14, 0, 3, 8 1/3

2: -4, -3, -2 1/2, -2 1/4, 3 1/4,

step-by-step explanation: