Explanation for Question 20 From the Math (No Calc) Section on the 2019 October Sat
Now looking at number 20, the last question of the no calculator section, 2 we can see that we're told that K is a constant. 3 And when they say that K is a constant, all they mean is that 4 K is just a normal number, 5 right? So it's a normal number and it's never going to change. 6 So no matter what value of X you have, 7 you could have negative 100 or positive. 8 100 is your X. It doesn't matter. K always is going to be the 9 same number. And then it goes on to ask us if the equation has 10 infinitely many solutions, what is the value of K? 11 And so the key for solving this question is knowing what it means to 12 have infinitely many solutions. If we have infinitely many solutions, 13 then that means that what's on the left of your equal side is the 14 same as what is on the right of your equal sign. 15 Always for example, two X is always going to be equal to two X, 16 right? Because no matter what X I put in, 17 it'll be the same on those sides. Also on the left, 18 right? We have three X plus one and three X plus one. 19 Those are both the exact same thing. So since they're both on different sides, 20 but they're the same expression, 21 then that means we have infinitely many solutions. 22 So we need to apply that knowledge to this question. 23 We have the equation two K X minus two is equal to X minus 24 two. And what we can notice immediately is that this side has an 25 X minus two. So that means that I need this left-hand side to 26 also be equal to X minus two, 27 b...