Question

if the linear equations ax+by+c=0 and lx+my+n=0 represent the same line and r=l/a=n/c write the value of r in terms of m and b

Answer 1

Answer:

r= m/b

Step-by-step explanation:

for same line a=l,b=m and n=c

Answer 2

$R = \frac{m}{b}$

Step-by-step explanation:

given : ax+by+c=0 ...(1)

lx+my+n=0..(2)

let assume

$\frac{l}{a}= \frac{n}{c} = k$

where k is a  non zero

thus l = ak  and n = ck

now , putting the value of l and n in equation 2

we get

lx+my+n = 0

akx+my+ck =0

now, taking common k we get

$k(ax+\frac{m}{k}y+c) =0$...(3)

ac+c = -by

put this in equation in 3

we get

$k(\frac{m}{k} -b)y=0$'

since k is a non zero term

then

$\frac{m}{k}-b = 0 \\\\k = \frac{m}{b}$

but , $\frac{l}{a}= \frac{n}{c} = k$

so , $R = \frac{m}{b}$

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