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

-3x + 1/2 y = -3

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.

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:

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

Hope this helps!

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