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 =

The answer is 6.

Step-by-step explanation:

Equation A:

y=6x-b

Equation B:

-3x+1/2y= -3

If the system of equation has infinite number of solutions then Equation A is equal to Equation B.

We will take equation B and move all the values to the R.H.S and isolate variable y

-3x+1/2y = -3

1/2y= -3 +3x

Multiply both sides by 2

2 * 1/2y = 2(-3+3x)

y = -6+6x

y = 6x-6 Equation B(I)

Now equate Equation A and Equation B(I)

6x-b = 6x-6

Subtract 6x from both sides.

6x-6x-b = 6x-6x - 6

-b = -6

Negative sign will be cancelled out by each other.

b = 6

Thus the answer is 6...