For the equations 5x – 6y = 2 and 10x = 12y + 7 ……………

Correct option is (A) There is no solution

Given system of equations is

5x – 6y = 2

\(\Rightarrow\) 5x – 6y - 2 = 0         _____________(1)

and 10x = 12y + 7

\(\Rightarrow\) 10x - 12y - 7 = 0      _____________(2)

By comparing with standard form of given system, we obtain

\(a_1=5,b_1=-6,c_1=-2\)

and \(a_2=10,b_2=-12,c_2=-7\)

\(\therefore\) \(\frac{a_1}{a_2}=\frac{5}{10}=\frac12,\)

\(\frac{b_1}{b_2}=\frac{-6}{-12}=\frac12\)

and \(\frac{c_1}{c_2}=\frac{-2}{-7}=\frac27\)

\(\because\) \(\frac12\neq\frac27\)

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

\(\therefore\) Given system has no solution.

Correct option is A) There is no solution