Question

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

Answer 1

Answer: 6

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Step-by-step explanation:

Let's solve the second equation for y to get it into slope intercept form.

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

Compare this to
`y = 6x-b` and we see that b = 6

Therefore, if b = 6, then the first equation will be exactly identical to the second original equation. The two equations would produce infinitely many solutions.

All of the infinitely many solutions would be of the form (x,y) = (x, 6x-6) where x is any real number.