Respuesta :
Answer:
For infinite many solution , b = [tex]\frac{1}{2}[/tex]
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 ,
[tex]\frac{a1}{b1}[/tex] = [tex]\frac{b1}{b2}[/tex] = [tex]\frac{c1 }{c2}[/tex]
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
[tex]\frac{-6b}{-3}[/tex] = [tex]\frac{1}{1}[/tex] = [tex]\frac{0}{3}[/tex]
∴ 6b = 3
So, b = [tex]\frac{3}{6}[/tex]
Hence b= [tex]\frac{1}{2}[/tex] Answer
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.
