In the given system of equations, $r $and $s$ are constants. The system has infinitely many solutions. What is the value of $\nicefrac{s}{r}$?
$\nicefrac{1}{2}y - 3x = -12$
$sy + rx = -36$
The correct answer is $\nicefrac{-1}{6}$ or -.1666 or -1.667 or….
current priority level - the Path to 700+ or higher
This is another QOTD for which we debated the current priority level. Given that there is only one current officially published question that is precisely like what’s here, it could be contended that only those of us on a Path to 750+ are really interested in this question.
Why we ended up giving it the level that we did is because maybe even doing a question like this once is enough to put it in your bag. Let us see.
One way to articulate what it means for a system to have infinitely many solutions is that one equation is a multiple of the other. Seeing that we would get -36 if we multiplied -12 by 3, and knowing that this system has infinitely many solutions, we can think that the bottom equation is the top equation multiplied by 3.
Knowing what we’re talking about here, we can then multiply $\nicefrac{1}{2}$ by 3 to determine that s is 1.5, and we can multiply -3 by 3 to determine that $r$ is -9.
Closing things out, we are unsurprised about the semi-random thing that we’re being asked to determine the value of(something that we do not take for granted). Dividing 1.5 by -9, we get our final answer, which we can choose to input as a fraction or as a decimal.
To close out a bit interactively, there is a particularly WRONG way to input our answer as a decimal. Do you know what that is? And, while you’re emailing us, do you actually also know another correct way the answer could have been input?