Answer with explanation:
Consider two linear equation in two variable,
ax + by =c
p x +q y=r
The 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 are
1. y= 6 x -b
→6 x -y -b=0
2. -3 x +y= -3
⇒-3 x+y+3=0
By 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.
