Correct option is (D) 4x + 6y – 11 = 0

The condition for inconsistent system of equations is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}.\)

(A) \(\frac{a_1}{a_2}=\frac24=\frac12,\)

\(\frac{b_1}{b_2}=\frac3{-6}=\frac{-1}2\)

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

\(\therefore\) System of equations is consistent.

(B) \(\frac{a_1}{a_2}=\frac22=1,\)

\(\frac{b_1}{b_2}=\frac3{1}=3\)

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

\(\therefore\) System of equations is consistent.

(C) \(\frac{a_1}{a_2}=\frac21=2,\)

\(\frac{b_1}{b_2}=\frac3{3}=1\)

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

\(\therefore\) System of equations is consistent.

(D) \(\frac{a_1}{a_2}=\frac24=\frac12,\)

\(\frac{b_1}{b_2}=\frac3{6}=\frac{1}2\) and

\(\frac{c_1}{c_2}=\frac{-5}{-11}=\frac5{11}\)

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

\(\therefore\) System of equations is inconsistent.

Hence, equation 4x + 6y – 11 = 0 is inconsistent to equation 2x + 3y - 5 = 0.

Correct option is D) 4x + 6y – 11 = 0