A system of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ is inconsistent (no solution) if the lines are parallel.$\frac{x}{2} + \frac{y}{3} - 5 = 0$$3x + 2y - 30 = 0$ ........(i)2x + ky - 7 = 0 .......(ii)Comparing coefficients:$a_1 = 3, b_1 = 2, c_1 = -30$$a_2 = 2, b_2 = k, c_2 = -7$Condition for inconsistency:$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$Apply the first part of the condition:$\frac{3}{2} = \frac{2}{k}$3k = 4$k = \frac{4}{3}$Check the second part:$\frac{3}{2} \neq \frac{-30}{-7}$ which is 1.5 ≠ 4.28The value of k is $\frac{4}{3}.$