Question

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

Answer 1

Answer:

For infinite many solution , b = $\frac{1}{2}$

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 ,

$\frac{a1}{b1}$ = $\frac{b1}{b2}$ = $\frac{c1 }{c2}$

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

$\frac{-6b}{-3}$ = $\frac{1}{1}$ = $\frac{0}{3}$

∴ 6b = 3

So, b = $\frac{3}{6}$

Hence b= $\frac{1}{2}$    Answer

Answer 2

Answer:

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.