Explanation
Correct answer: B.
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 -coefficient to the -coefficient for one equation is equivalent to the ratio of the -coefficient to the -coefficient for the other equation. This ratio for the given equation is to , or to . Only choice B is an equation that isn't equivalent to the given equation and whose ratio of the -coefficient to the -coefficient is to .
Desmos solution:
Note: The blue line is the given equation; the green line has the same slope but a different intercept, so the system has no solution.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. Multiplying each of the terms in this equation by yields an equation that is equivalent to the given equation. This system would have infinitely many solutions.
Choice C
Choice C is incorrect. The ratio of the -coefficient to the -coefficient in is to , or to . Since this ratio is not equivalent to that for the given equation, this system would have exactly one solution.
Choice D
Choice D is incorrect. The ratio of the -coefficient to the -coefficient in is to , or to . Since this ratio is not equivalent to that for the given equation, this system would have exactly one solution.