Question

please can you help me!!​

Answer 1

Knowledge required:-

When two linear equation in two variables are given as

a₁x + b₁y + c₁ = 0   &

a₂x + b₂y + c₂ = 0

then,

for intersecting lines

$\bf{\frac{a_1}{a_2} \neq \frac{b_1}{b_2} }$

for parallel lines

$\bf{\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}}$

for coincident lines

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

Answer to the given question :-

we are given with two linear eqns in two variables that are

$\tt{18x-7y-24=0}$

and

$\tt{\frac{9}{5}x-\frac{7}{10}y-\frac{9}{10}=0}$

so, by comparison

a₁ = 18 ; b₁ = -7 ; c₁ = -24

a₂ = 9/5  ; b₂ = -7/10 ; c₂ = -9/10

so,

$\tt{\frac{a_1}{a_2}=18*\frac{5}{9} = 10 }$

$\tt {\frac{b_1}{b_2}=-7*\frac{-10}{7} = 10 }$

$\tt{\frac{c_1}{c_2}=-24*\frac{-10}{9}=\frac{80}{3}}$

from here we concluded that

$\bf{\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2} }$

Hence,

the Lines will be parallel to each other.