Explanation for Question 29 From the Math (Calc) Section on the 2019 May Sat
So question 29 says in this system of equations below a and 2 C or constant, if the system of equation has an infinite number of solutions, 3 what is the value of a and before we even start solving this problem, 4 there's actually a typo. Um, and how this is written. 5 This is supposed to say a X plus Y equals C. 6 So now we can start solving this problem. 7 The first thing that you need to take note of is that the system 8 of equations has an infinite number of solutions. 9 So if two lines or two equations have an infinite number of solutions, 10 that means that they're the same line. So their equations should have the same 11 slope and the same Y intercept. 12 So with that in mind, all we need to do is solve for the 13 slope of the top line. And then we can input that into the bottom 14 equation. 15 So let's start by putting the first line into Y MX plus B form. 16 So we have one half X plus one third, 17 Y equals one over six. 18 So first we need to subtract, uh, 19 one half action, both sides. So that gives us one third, 20 Y is equal to negative one half packs, 21 uh, plus one six, it's a negative one half X plus 22 one six, and then we have to multiply both sides by three. 23 And we get one, as he pulled in negative three, 24 over two X 25 plus three, over six, which is just equal to two plus 26 two. And so now we know that the slope of both lines 27 needs to be negative three over two. So now let's take a X plus 28 Y equals C and let's put that into Y equals Y equals 2...