For a pair of linear equations and

MATHEMATICS · Single correct · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables

Problem

For a pair of linear equations

a_1x + b_1y + c_1 = 0

and

a_2x + b_2y + c_2 = 0

, which of the following conditions guarantees infinitely many solutions? (a)

\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}

(b)

a_1b_2- a_2b_1=0

(c)

\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}

(d)

\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}