Explanation for Question 13 From the Math (No Calc) Section on the 2020 October Sat
So question number 13 gives us an equation that has one piece missing. 2 It has a K where, where you're supposed to come up with a number 3 and they ask us for which value of K would we not have exactly 4 one solution, not have exactly one solution. 5 And so whenever you see us or someone asking you about the number of 6 solutions, you're also always going to want to think about infinite solutions and 7 no solutions in thin knit, 8 infinite solutions and no solutions. Now, 9 if there's infinite solutions, both sides of the equations are the same. 10 For example, two equals two. This is always true. 11 So you'll have infinite solutions, something that has no solutions is never 12 true. For example, two equals three, two never equals three. 13 They're two totally different numbers. So that would have no solution. 14 And so if we want our answer to have one solution, 15 then we can try to find a case in which there are either infinite 16 or no solutions. 17 And then that will be our answer, right? Because if I have either of 18 these cases, then I don't have one solution. 19 Now, if I want to try and make both sides of my equation, 20 the same, what needs to go in front of the X is three, 21 right? Because if I want these to be exactly equal to each other, 22 then my cane needs to be three. This is a case where I have 23 infinitely many solutions. I have more than one solution. 24 And so our correct answer that does not give us a single value or 25 a single solution is going to be C three.