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y = 6x+3 One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which equation could be the second equation in this system? y = 2(6x) +3
Correct answer: D (parsed from the explanation — this source omits an answer key for this item)
Explanation
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 2 =2 6 +3 2 =2 6 +3 yields ^yh ^ x h. Thus, ^yh ^ x h 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.
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