Correct option is (A) 3x – y = 1, 6x – 2y = 5

(A) \(\frac{a_1}{a_2}=\frac36=\frac12,\)

\(\frac{b_1}{b_2}=\frac{-1}{-2}=\frac12\)

and \(\frac{c_1}{c_2}=\frac{-1}{-5}=\frac15\)

\(\because\) \(\frac12\neq\frac15\)

\(\therefore\) \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)

Therefore, this system has no solution.

Hence, this system of equations is inconsistent.

(B) \(\frac{a_1}{a_2}=\frac4{12}=\frac13,\)

\(\frac{b_1}{b_2}=\frac{6}{18}=\frac13\)

and \(\frac{c_1}{c_2}=\frac{-7}{-21}=\frac13\)

\(\therefore\) \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)

\(\therefore\) This system has infinitely many solutions.

Hence, this system of equations is consistent.

(C) \(\frac{a_1}{a_2}=\frac49,\)

\(\frac{b_1}{b_2}=\frac98\)

\(\because\) \(\frac49\neq\frac98\)

\(\therefore\) \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)

\(\therefore\) This system has unique solution.

Hence, this system of equations is consistent.

(D) \(\frac{a_1}{a_2}=\frac49,\)

\(\frac{b_1}{b_2}=\frac{12}{9}=\frac43\)

\(\because\) \(\frac49\neq\frac43\)

\(\therefore\) \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)

\(\therefore\) This system has unique solution.

Hence, this system of equations is consistent.

Correct option is A) 3x – y = 1, 6x – 2y = 5