Question

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

Answer 1

If the value of b is 6 then the system will have an infinite number of solutions since they will be the same lines.

Answer 2

Answer with explanation:

A system of equation will have infinite number of solution

if both the equation of line are coincident.

6 x - y=b

-3 x + y = -3

Line, ax + by=c

p x + q y =r,

are said to be coincident , if

$\frac{a}{p}=\frac{b}{q}=\frac{c}{r}\\\\ \frac{6}{-3}=\frac{-1}{1}=\frac{b}{-3}\\\\{\text{as}} \frac{6}{-3}\neq\frac{-1}{1}$

So,there is no real value of b for which , we can make the system of equation coincident or infinite umber of solutions.