The system of equations 2x - 3y - 5 = 0 , 15y - 10x + 50 = 0

Step-by-step solution

The given system of equations is: 2x - 3y - 5 = 0 -10x + 15y + 50 = 0 Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 , we have: a₁ = 2 , b₁ = -3 , c₁ = -5 a₂ = -10 , b₂ = 15 , c₂ = 50 Calculating the ratios of the coefficients: a₁ a₂ = 2 -10 = - 1 5 b₁ b₂ = -3 15 = - 1 5 c₁ c₂ = -5 50 = - 1 10 Since a₁ a₂ = b₁ b₂ c₁ c₂ , the lines represented by the equations are parallel and distinct. Thus, the system of equations has no solution and is inconsistent.