One of the two equations in a linear system is . The system has no solution. Which of the following could be the other equation in the system?
-
A
-
B
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C
-
D
Correct answer: B
Explanation
Choice B is correct. A system of two linear equations written in standard form has no solution when the equations are distinct and the ratio of the x-coefficient to the y-coefficient for one equation is equivalent to the ratio of the x-coefficient to the y-coefficient for the other equation. This ratio for the given equation is 2 to 6, or 1 to 3. Only choice B is an equation that isn’t equivalent to the given equation and whose ratio of the x-coefficient to the y-coefficient is 1 to 3.
Choice A is incorrect. Multiplying each of the terms in this equation by 2 yields an equation that is equivalent to the given equation. This system would have infinitely many solutions. Choices C and D are incorrect. The ratio of the x-coefficient to the y-coefficient in (choice C) is
to 2, or
to 1. This ratio in
(choice D) is 6 to 2, or 3 to 1. Since neither of these ratios is equivalent to that for the given equation, these systems would have exactly one solution.
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