Question

24
are two lines
5
. The graphs of the equations 5x – 15y = 8 and 3x – 9y
which are
(a) coincident
(b) parallel
(c) intersecting exactly at one point​

Answer 1

Question :-

The equations $5x -15y = 8$ and $3x - 9y -\frac{24}{5} =0$ which are

(a) coincident

(b) parallel

(c) intersecting exactly at one point​

(d) perpendicular to each other

Answer :-

DATA:-

$5x -15y-8 = 0$     ______________{1}

$3x - 9y -\frac{24}{5}=0$_____________{2}

The eq.'s are in the form of linear equation in two variables that is,

$a_1x+b_1y+c_1= 0 \\a_2x+b_2y+c_2=0$

Let's simplify this

$\frac{a_1}{a_2} = \frac{5}{3}$

$\frac{b_1}{b_2} =\frac{15}{9} = \frac{5}{3}$

$\frac{c_1}{c_2} = \frac{-8}{-\frac{24}{5} }= \frac{-8*5}{-24} = \frac{40}{24}=\frac{5}{3}$

Hence, $\frac{a_1}{a_2} =\frac{b_1}{b_2} =\frac{c_1}{c_2}$

∴ The lines are coincident

Hence option (a) is correct

THANK YOU!!