A coordinate grid with a line labeled negative 3 x plus StartFraction one-half EndFraction y equals negative 3 and passes through the points (1, 0) and (0, negative 6). What value of b will cause the system to have an infinite number of solutions?

y = 6x – b

–3x + StartFraction one-half EndFractiony = –3

b =

2
4
6
8

C

Step-by-step explanation:

Given that the line -3x + y/2 = -3 passes through the points (1, 0) and (0, -6).

First rearrange the equation

-3x + y/2 = -3

Y = 2( 3x - 3 )

Y = 6x - 6 (1)

Also, the slope of points (1, 0) and (0, -6). Will be

M = ( -6 - 0 )/( 0 - 1 )

M = -6/-1

M = 6

Using general linear equation

Y = MX + C

Let Y = 0 and X = 1

0 = 6(1) + C

C = -6

Substitutes C back into the equation

Y = 6x - 6 (2)

The value of b that will cause the system to have infinitely many number of solutions is 6

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step-by-step explanation: