Question

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

number of solutions?
y = 6x-b

-3x + 1/2 y = -3

Answer 1

Hi there!

The way that an infinite number of solutions is achieved is when the two equations, when solved together, get an answer which is just a number equal to the same number. To do this, first substitute 6x-b in for y in the second equation.

`-3x+(1)/(2)(6x-b)=-3`

`-3x+3x-(1)/(2)b=-3`

`-(1)/(2)b=-3`

Now, we see that b needs to be equal to -3 when multiplied by -1/2. When both sides are divided by -1/2, b becomes equal to 6. Thus, b must be 6.

Check work:

`6x-6=y`

`-3x+(1)/(2)(6x-6)=-3`

`-3x+3x-3=-3`

`-3=-3`

Thus, as they are equal to each other, the answer is correct. b = 6.

Hope this helps!