What value of b will cause the system to have an infinite number of solutions? y = 6x – b –3x + y = –3 b =(a)2(b) 4(c) 6(d) 8

Accepted Solution

Answer with explanation:Consider two linear equation in two variable, ax + by =c p x +q y=rThe equations have an infinite number of solutions , means the two lines are Coincident, when it follows the following law [tex]\frac{a}{p}= \frac{b}{q}= \frac{c}{r}[/tex]                                       --------------------------------------(1)Now, equation of two lines are1. y= 6 x -b→6 x -y -b=02. -3 x +y= -3 ⇒-3 x+y+3=0By the above law,that is law 1, the two lines will be coincident [tex]\frac{6}{-3}=\frac{-1}{1}= \frac{-b}{3}\\\\2=1= \frac{b}{3}[/tex]Which is not possible that is ,2≠1.→→→Hence the two lines can never be coincident for any value of b.