OG详解-OG7 数学1 Q32

Choice D is correct. It’s given that the system has infinitely many solutions. A system of two linear equations has infinitely many solutions when the two linear equations are equivalent. When one equation is a multiple of another equation, the two equations are equivalent. Multiplying each side of the given equation by 2 yields 2(y) = 2(6x+3). Thus, 2(y) = 2(6x+3) is equivalent to the given equation and could be the second equation in the system.
Choice A is incorrect. The system consisting of this equation and the given equation has one solution rather than infinitely many solutions. Choice B is incorrect. The system consisting of this equation and the given equation has one solution rather than infinitely many solutions. Choice C is incorrect. The system consisting of this equation and the given equation has no solutions rather than infinitely many solutions.