What value of b will cause the system to have an infinite
number of solutions?
y = 6xb
-3x +
y = -3

A system of equations has infinite solutions when we have more variables than linear independent equations.

This means that if we want to have infinite solutions, we need to find a value of b such the two equations are linear dependent, his means that the equations are the same, or that one equation is a scalar times the other, like x + y = 2. and 2x + 2y = 4 (the second is 2 times the first one)

Here we have the equations:

y = 6xb - 3x

y = -3x

(the second equation actually says y = -3, but this may be written wrong)

So we want that both equations are the same (because in both cases we have y equals something), for this, we need to find the value of b:

6xb - 3x = -3x

6xb = - 3x + 3x = 0

and this must work for every value of x, so we must have that b  = 0.

For infinite many solution , b =

Step-by-step explanation:

Given two linear equation as,

- 6bX + Y +0 =0             and

-3X + Y + 3 =0

Here given that system have infinite number of solutions

Now for infinite number of solutions ,

= =

Thus from given linear equation ,the coefficient of both equation be ,

a1 = -6b       b1 = 1     c1 = 0           for -6bX + Y + 0 = 0

a2 = -3         b2 = 1    c2 =3            for -3X + Y + 3 = 0

SO, from the condition of infinite solutions

= =

∴ 6b = 3

So, b =

Hence b=    Answer

b.my answer is b.

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two? xd

step-by-step explanation: