Given system of equations is
2x - 3y = 7
(a + b)x - (4a + b)y = a + b -3
system has no solution if \(\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)
\(\Rightarrow\) \(\frac{2}{a + b} = \frac{-3}{-(4a + b)}\) \(\neq \frac{7}{a + b -3}\)
\(\Rightarrow\) \(\frac{2}{a + b} = \frac{3}{4a + b}\)
\(\Rightarrow\) 2(4a + b) = 3(a + b)
\(\Rightarrow\) 8a + 2b = 3a + 3b
\(\Rightarrow\) 5a - b = 0
\(\Rightarrow\) b = 5a
Also \(\frac{2}{a + b} \neq \frac{7}{a + b - 3}\)
\(\Rightarrow\) 2a + 2b - 6 \(\neq\) 7a + 7b
\(\Rightarrow\) 5a + 5b \(\neq\) -6
\(\Rightarrow\) b + 5b \(\neq\) -6
\(\Rightarrow\) 6b \(\neq\) -6
\(\Rightarrow\) b \(\neq\) -1
Hence, given system has no solution if a and b satisfies the equation b = 5a but b \(\neq\) -1.