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.
