NDA Mathematics Question (2025) — Solution

Step-by-step solution

The given system of equations is: 2x - 3y - 5 = 0 -10x + 15y + 50 = 0 Comparing with a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0, we have: a_1 = 2, b_1 = -3, c_1 = -5 a_2 = -10, b_2 = 15, c_2 = 50 Calculating the ratios of the coefficients: a_1 a_2 = 2 -10 = - 1 5 b_1 b_2 = -3 15 = - 1 5 c_1 c_2 = -5 50 = - 1 10 Since a_1 a_2 = b_1 b_2 c_1 c_2 , the lines represented by the equations are parallel and distinct. Thus, the system of equations has no solution and is inconsistent.